Two young children were injured in the crash, one seriously, according to television station KSHB in Kansas City, Missouri.
The Kansas City Police Department said a collision had occurred on Thursday when a truck hit two stationary vehicles and injured two children.
Police said the driver of the truck was treated for non-life threatening injuries but would not confirm if it was Reid. No one involved was charged.
The Chiefs are scheduled to travel on Saturday to Tampa for Sunday’s Super Bowl against the Buccaneers.
“The organization has been made aware of a multi-vehicle accident involving outside linebackers coach, Britt Reid,” the team said in a statement.
“We are in the process of gathering information, and we will have no further comment at this time. Our thoughts and prayers are with everyone involved.”
The Chiefs did not respond to a request for comment.
The 35-year-old Reid has been with the team since his father was hired by the franchise in 2013. Reporting by Rory Carroll in Los Angeles and Amy Tennery in Tampa; Editing by Peter Rutherford and Kim Coghill