No one was hurt in Thursday morning's crash on a highway off-ramp near the team's stadium in South Philadelphia.
Police say the car's driver was driving too fast when he spun out and hit a concrete barrier around 2:30 a.m. The driver failed field sobriety testing and was arrested on DUI charges. Celek is not facing charges.
Celek, who turned 27 on Wednesday, released a statement through the team saying he exhibited "extremely poor judgment."
"I did not know that the person driving the car was over the legal limit, but that's not an excuse. I put my life in danger and was in a vehicle that put other people's lives in danger, and that's just not the way I operate. It will not happen again," he said in the statement, according to the Philadelphia Daily News.
Celek caught 62 passes for the Eagles last season, including five touchdown catches. He had surgeries to repair a torn labrum in his left hip and for a sports hernia earlier this month.
Information from The Associated Press was used in this report.