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 turned 27 on Wednesday. He caught 62 passes for the Eagles last season, including five touchdown catches.
"The team is aware of the accident and has been in contact with Brent," the team said in a statement emailed to CBSSports.com. "Thankfully, no one involved in the accident was injured and, to our knowledge, Brent is not facing any legal charges."
Celek released a statement through the team saying he exhibited "extremely poor judgment." He said he didn't know the driver was drunk but that's not an excuse. He promises to never let it happen again.