Lower Saucon Township police said Parker was a passenger in a vehicle that was stopped for a traffic violation at 12:33 a.m. ET near Lehigh University, where the Eagles train.
Parker was carrying "a small amount of marijuana" and was taken to Northampton County Prison, police said. Parker was released after posting $1,000 bail later Wednesday morning, a prison official said.
Eagles coach Andy Reid said he was aware of the incident.
"It's in the law's hands right now. As time goes on, I'll know more," Reid said.
Reid said the team curfew was 1 a.m. ET.
The 31-year-old Parker played four seasons with Tennessee before joining the Eagles in 2005. He was a full-time starter last year for the first time in his career, finishing with five sacks, 76 tackles and one interception that he returned 55 yards for a touchdown in a win over San Francisco.
Parker is listed as the team's starting left defensive end, but the Eagles regularly rotate their linemen. He didn't practice Wednesday morning because Reid gave players over age 30 the session off.
Parker legally changed his name from Juqua Thomas in 2008 to fulfill a request by his late father.