The 26-year-old England tight-head prop, who was sent off, pleaded guilty at a disciplinary hearing on Tuesday.
Brookes will miss Saints' Premiership game at Leicester on Saturday and their Champions Cup game with Leinster.
Newcastle lock Calum Green, 26, has also been banned for a week after admitting striking with his arm.
Green, who will miss Falcons' home game with Harlequins on Sunday, struck Brookes with his forearm during the same game and was cited by the citing commissioner after the incident was missed by referee Andrew Jackson.
Brookes was dismissed in the 38th minute of Saints' 22-16 defeat when he charged into the ruck and struck the head of Newcastle hooker Scott Lawson with his shoulder.
Northampton's Kieran Brookes has been banned for two weeks after admitting charging into a ruck without using his arms in Friday's loss to Newcastle.