The 20-year-old has featured once for the Canaries' Under-21 side in the EFL Trophy this season, having joined from Dartford in February.
Midfielder Adams played four times in the Conference Premier for Dartford in the 2014-15 season.
Braintree are hoping they will be able to extend the deal to the end of the season once he turns 21 in January.
Braintree Town have signed Norwich City youngster Ebou Adams on month-long youth loan.