It means the Rovers chief will be absent from the dugout for Saturday's home fixture with Wycombe Wanderers and the trip to Gillingham the following Tuesday.
The charge was issued after Wellens was red carded for dissent in Doncaster' s defeat to Plymouth Argyle at the end of last month.
Wellens felt aggrieved by the late penalty decision which saw his side fall to a 2-1 defeat at Home Park.
In a hearing last week, Wellens admitted breaching FA Rule E3, which states "an individual shall at all times act in the best interests of the game and shall not act in any manner which is improper or brings the game into disrepute or use any one, or a combination of, violent conduct, serious foul play, threatening, abusive, indecent or insulting words or behaviour.”
The Doncaster manager has also been fined £1,000.