A typical humanoid creature with the special ability wild shape does not meet the prerequisites of the feat Mighty Roar and also may not meet the requirements set forth by the feat's type...
Although some feats are listed in the section Monster Skills and Feats in the Monster Manual, those feats are only "typically only used by monsters" (303), so those feats are available to PCs who meet the feats' prerequisites.
However, the feats in question aren't in the Monster Manual but in Savage Species, so two other issues need addressing.
Meeting the feats' prerequisites
The Player's Handbook on Prerequisites says
Some feats have prerequisites. Your character must have the indicated ability score, class feature, feat, skill, base attack bonus, or other quality designated in order to select or use that feat. [...]
A character can’t use a feat if he or she has lost a prerequisite. For example, if your character’s Strength drops below 13 because a ray of enfeeblement spell, he or she can’t use the Power Attack feat until the prerequisite is once again met. (87)
Feats are selected upon advancing a level as part of the standard level-up process as per Level Advancement (PH 58-9), and prerequisites must be met right then. The Dungeon Master's Guide says that
You may want to award experience points at the end of each session, or you might wait until the end of each adventure. That’s up to you. However, the standard procedure is to give them out at the end of each session, so players whose characters go up a level have time to choose new spells, buy skills, and take care of other details related to level advancement. (18)
Thus, while the nuts and bolts of advancement occur between sessions, the XP awarded at the session's end is what determines if a creature advances a level and effects affecting the creature when that session ends determine if the creature meets a feat's prerequisite.
Yes, that's crazy and can lead to more than a little stupid if the DM is unreasonably strict.1 But it does mean, for example, a druid wanting to pick the feat Multiattack (MM 304) must meet that feat's prerequisites (probably by using the special ability wild shape) when a session ends during which the druid gained enough XP to advance a level.
By the same token, a druid that wanted to take the feat Mighty Roar (Savage Species 37) must meet that feat's prerequisites of the animal or magical beast type and Large or bigger size at the session's end, a difficult task. (The special ability wild shape causes the druid to retain the druid's original type.)2
Dealing with the feat type monstrous
The Savage Species (Feb. 2003) description of feats with the type monstrous says
Many of the feats described in this chapter belong to a new category, monstrous feats (see the second half of Table 4–1, on page 32). Only creatures with a monstrous form or one or more monstrous abilities may select these feats. Monstrous forms and abilities are those that are unavailable to normal humanoid or animal creatures, including but not limited to extra appendages, nonstandard appendages (such as tentacles or a tail), supernatural abilities, and spell-like abilities. With your DM’s permission, you may be able to choose monstrous feats for your character if your character acquired unusual abilities through transformation or by advancing in a prestige class. (29)
Emphasis mine. This could mean monstrous form as in the creature can use the supernatural ability alternate form (on which wild shape is based) or change shape to assume a monstrous form, but the DM could also read it as the creature needing to be a literal monster all the time. Then the creature, if a PC, also needs the DM's permission. (Similar language is used in the Draconomicon (Nov. 2003)—another source of many monstrous feats—, while Serpent Kingdoms (June 2004) directs readers to Savage Species for monstrous feats, providing no definition.)
However, the PC may eventually want a monstrous feat from Libris Mortis (Nov. 2004), that text's monstrous feats definition saying
A few of the feats in this chapter belong to the category of monstrous feats. Only creatures and characters with a monstrous form or one or more monstrous abilities may select these feats. Monstrous forms and abilities are those that are typically unavailable to humanoid or animal creatures, including but not limited to extra appendages, nonstandard appendages, and extraordinary, supernatural, or spell-like abilities.
Although some characters will be unable to take these feats initially, later events (such as acquiring an undead template or multiclassing into an undead monster class) might allow access to these specialized feats. (23-4)
Emphasis mine. Thus the DM's permission isn't required for these feats. Finally, Magic of Incarnum (2005) shortens its definition to
Monstrous feats require a creature to have a monstrous form or special abilities. (34)
probably so as not to waste page space giving a detailed definition of the feat type when that text contains only one feat of that type, Undead Meldshaper (MoI 41).
The strict DM has two choices:
The DM can elect to have the definition of monstrous feats from Magic of Incarnum (which is largely useless and serves no purpose beyond assigning the feats a type other than general), be, as the last printed definition, the final word on monstrous feats.
Under this ruling, for example, a druid that meets the prerequisites of the feat Mighty Roar can take feat Mighty Roar.
The DM may have each text's definition of monstrous feats apply to the monstrous feats in that text (e.g. only monstrous feats from Savage Species use the Savage Species definition), making things more complicated but giving the strict DM permission to nix PCs taking some feats having the type monstrous.
Under this ruling, for example, a druid that meets the prerequisites of the feat Mighty Roar can still be denied the feat Mighty Roar by the DM because the Savage Species definition of the feat allows DM to.3
Besides feats with the type monstrous, other feat types also have variable definitions depending on the definition's source (e.g. ambush feats, divine feats, vile feats), so making such a choice may set a precedent for the campaign.
...But allowing a druid to take the feats anyway won't be disruptive
The feats Mighty Roar and Greater Mighty Roar collectively allow a once per day non-mind-affecting, non-fear effect that can render foes within 30 ft. of the user shaken or panicked, respectively, if foes fail a Willpower saving throw. That's only cool, and nothing compared to what the druid could have done with those two feats. A house rule changing or even eliminating those feats' more restrictive prerequisites is not a big deal.
1 "Remember, Blackleaf is poisoned," says the DM, "and that 1 point of Strength damage drops your score to 12, so you can't take the feat Power Attack when you level up like you wanted. See you next week!" (Seriously, don't sock him—just count to 10 and walk away.)
2 A druid who ends a session while affected by the 1st-level Drd spell aspect of the wolf [trans] (SpC 16-17) and the 5th-level Drd spell animal growth [trans] (PH 198) meets the prerequisites of the feat Mighty Roar (SS 37), but such effects must be duplicated were the druid to want to meet subsequently the prerequisites of the feat Greater Mighty Roar (SS 35).
3 No, I don't know why the DM would be a jerk about the feat Mighty Roar, but he might want to restrict a PC's access to something like, for example, the feat Improved Rapidstrike (Dr 70-1).