It's not that bad, glue and screw. Remove the inner board from the drawer front and reattach it to the drawer first. You might have to clean up the MDF a bit. Use filler if you have to, maybe, but don't use nails. Then reattach the drawer front - again with screws. It might not look perfect, but it'll probably look fine when the drawer is closed. Consider wood block fillets at the interior corners (sacrificing a bit of space).

Alternatively you could rebuild the drawer frame, using the same drawer front so it matches.