Tupai was sin-binned in Saints' league appointments with Newcastle, Sale Sharks and Gloucester, which meant an appearance before Rugby Football Union disciplinary chiefs in Bristol.
The suspension rules 32-year-old Tupai out of EDF Energy Cup games against Worcester and Newport Gwent Dragons.
It is the latest worry for an injury-hit Northampton squad that suffered a succession of blows during the past four days.
Captain Bruce Reihana will undergo knee surgery tomorrow and is unlikely to play again until January, while Saints' England hooker Steve Thompson has a torn calf muscle and props Tom Smith and Pat Barnard were also hurt during the 28-7 defeat against Gloucester last Saturday.
And just to compound Northampton's front-row problems, hooker Matias Cortese suffered an ankle injury in a Guinness A League game on Monday night that could mean four weeks out.