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. ET. The driver failed field sobriety testing and was arrested on DUI charges.
In a statement issued through the Eagles obtained by the Philadelphia Inquirer, Celek said, "As far as the events of last night are concerned, the bottom line is I showed 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."
Celek turned 27 on Wednesday. He caught 62 passes for the Eagles last season, including five touchdowns.
"Thankfully, no one was injured and, to our knowledge, Brent is not facing any legal charges," a team spokesman told the newspaper.
The Associated Press contributed to this report.