Megson was sent to the stands for one protest too many after a penalty appeal for his side was turned down during Saturday's 1-1 draw at Dagenham & Redbridge.
The former West Brom and Bolton boss had earlier been infuriated by referee Steve Rushton's decision to award Dagenham a penalty for handball in the 80th minute.
Megson, installed by Owls chairman Milan Mandaric as Alan Irvine's replacement, has won only two of his 12 games in charge since taking over in early February.
He has until 4pm on Thursday, March 31 to respond to the charge.
Source: PA
Source: PA