The New Zealander, 32, will miss three matches, including a European Champions Cup trip to his former club Leinster.
Gopperth will also miss his side's next two home games, against Gloucester in the Premiership this Sunday and Toulon.
Wasps have already appealed against the length of Gopperth's suspension.
Gopperth caught Tait on the side of the head with a rabbit punch as he chased his own up and under in the 54th minute.
He did come back on the pitch again briefly after his time in the bin, but was replaced for the final 10 minutes by Alex Lozowski.
Gopperth was initially yellow-carded by referee Tim Wigglesworth on Sunday, before being summoned to appear before a three-man Rugby Football Union disciplinary panel at a Coventry hotel on Tuesday evening, for 'punching or striking, contrary to law 10.4(a)', to which he pleaded guilty.
The appeal hearing will be held on Thursday, before which the club are unable to make any further comment.
The former Junior All Black is in his second stint in the Premiership, having first left New Zealand in 2009 to sign for Newcastle, where he spent four years before moving to Leinster in 2013.
Wasps stand-off Jimmy Gopperth has been handed a three-week ban for his late challenge on Leicester captain Mathew Tait in his side's 24-16 Premiership defeat at Welford Road on Sunday.