The NFL said Meriweather had been suspended without pay a day after he was penalized for hits on Chicago's Alshon Jeffery and Brandon Marshall in a 45-41 home win over the Bears.
He was also fined for earlier this season, drawing a $42,000 penalty after using his helmet to bring down an opponent in a game against Green Bay.
The league said Meriweather was cited for "repeat violations this season of NFL safety rules prohibiting hits to the head and neck area of defenseless players, including two in Sunday's Washington-Chicago Bears game."
If the suspension is upheld, he would miss upcoming games at Denver and at home game against San Diego.
If Meriweather appeals, the NFL said it will hold an expedited hearing with a decision requested before Washington's next game.