Yes, this should work
Regeneration in general says:
Damage dealt to the creature is treated as nonlethal damage, and the creature automatically cures itself of nonlethal damage at a fixed rate per round, as given in the creature’s entry.
And the exception for the Solar's regeneration is
A solar takes normal damage from epic evil-aligned weapons, and from spells or effects with the evil descriptor.
Alignment for weapons is a magical property of the weapon, and if the magic properties are suppressed by Antimagic Field, they won't work. Likewise, magical effects and spells will be suppressed in the field.
P.S. I originally thought that an inherently evil creature could work. However the rules for these are:
A creature with an alignment subtype (chaotic, evil, good, or lawful) can overcome this type of damage reduction with its natural weapons and weapons it wields as if the weapons or natural weapons had an alignment (or alignments) that match the subtype(s) of the creature.
So, rules as written, these creatures only overcome damage reduction effects, and what's protecting the Planetar here is regeneration, not damage reduction. (Of course, a DM can rule it also applies to regeneration, but then, a DM can rule whatever they want).
P.S.S. While it is unkillable by damage while in the field, that does not mean you cannot kill it. The solar will still be unconscious when at 0 hit points. You could keep pummeling it to keep it K.O., drag it out of the antimagic field or dead magic zone, and kill it there. Suffocating it (see this answer) also would work, even in the field.