Braid pleaded guilty to striking Nizaam Carr twice, the first with his forearm to the back of the neck and the second with a part-open hand to the head, while Carr was on the ground in the 62nd minute of the Blues' 27-17 defeat last weekend.
He will miss all rugby until April 6.
It amounts to only two games, however, given the Blues have a bye in that period.
They have a bye after they host the Hurricanes on Friday. The Blues then play the Rebels in Melbourne on April 5 before hosting the Sharks the following weekend.
Sanzar judicial officer Mike Heron considered handing down a five-week ban to Braid but felt three weeks was appropriate given Braid's clean judicial record in the five years he has played Super Rugby.
Carr was lying on the ground at the time of the incident and wasn't able to avoid the blows. Heron accepted the fact the force was not severe and the impact not significant. Braid accepted the conduct was intentional, but explained it resulted from his frustration with the Stormers' player and his belief that the player was infringing at a critical time and place in the match.
The Blues are already missing a host of players. All Blacks Jerome Kaino (shoulder), Anthony Boric (neck), Isaia Toeava (hip) and Rudi Wulf (shoulder) as well as George Moala (shoulder) and David Raikuna (hamstring) missed the Stormers match through injury, and Rene Ranger (suspended), Tony Woodcock and Michael Hobbs (both unavailable) were absent. Woodcock is expected to play this weekend.
