In short, yes.
There are a few things that make monk on par with the other melee fighting classes. I'll list a few of them here:
Dex to attack and damage
Monks can apply dex to attacks and damage automatically at level one.
Monks are the only class that gets 2 attacks per round at level 1, and they keep up with Fighter attacks per round all the way to 20.
Class features apply to monk weapons
What counts as a monk weapon has been expanded a lot, and most of the monk class features (including increased damage) apply to monk weapons and unarmed strikes equally. In addition, the slew of exotic weapons that monks used to get have been condensed into reflavours of simple weapons. For example, nunchaku are now mechanically clubs, rather than a separate weapon type.
Monks in 5e have much less of a Multiple Attribute Dependency problem. Since monks get Dex to attack and damage for free, Strength is largely unnecessary. Int and Cha are as useful as they were in 3e. There are a few things that Int and Cha are useful for in both systems, but they're hardly essential.
Wisdom affects the same sort of stuff in 5e as it did in 3e, but it's less important due to other mechanical changes. Since "flat-footed" doesn't cause you to lose Dex Ac anymore, using Dex to increase AC is just as good as increasing Wis. You can probably end up with similar AC as a fighter by then end game.
Monks need to care about 3 stats, but they have basically the same number of dependencies as a fighter or barbarian. The fighter and barb both need Str and Con, with a secondary focus on Dex, and a monk needs Dex and Wis, with a secondary focus on Con. Since the stat cap is 20, it's actually not difficult to have a 20 and a couple 16-18s, as well as a 12 or two.
Better class features
The monk class features in 5e are similar to the ones in 3e, but they're a bit better, and a bit more reliable than they were before. I haven't done any real analysis on this, this is really just based on a first glance.
There are three monk paths in the PHB, all of which do cool things. There's one for a classic monk that's similar to the one in 3e, but the other two add some really interesting things to the class that broaden the kind of situations that the monk can handle, which is a problem that mundane classes have had since the dawn of time. :)
Broadly speaking, the monk does less damage than the Barbarian, and has less tanking ability than the Fighter, but is a very strong and versatile mobile melee fighter. A better character optimizer might have a different opinion, but as a player who doesn't make broken characters, the monk looks like it's on par with the Barbarian and Fighter.