Cooley was hurt on the first play of the second quarter. He limped to the sideline but was later carted off to the locker room. He caught two passes for 21 yards before leaving.
The news is another blow to a Redskins offense that already was without starting linemen Chris Samuels and Randy Thomas. Washington (2-5) has failed to score more than 17 points in any game this season.
"When it rains, it pours," center Casey Rabach said. "We just keep taking hits on the offensive side of the football."
Cooley went to the Pro Bowl after each of the last two seasons and has never missed a game since entering the NFL in 2004.
"Losing Chris is big," Campbell said.
Information from the Associated Press was included in this report.