It will fit the Aero M4 upper receiver, but it will not fit an M4E1 upper receiver as it requires a proprietary Aero barrel nut.
The first answer stating that this does not work with the Aero Precision M4E1 upper is INCORRECT. It will work with the M4E1 Threaded Upper but it will NOT WORK with the M4E1 Enhanced Upper.
It will fit as long as it not the enhanced version. The enhanced version utilizes a proprietary barrel nut and rail mounting system and requires the use of an Aero Precision handguard made for that setup.