Smith had pulled over after his vehicle, a 2019 Lamborghini in which Cordero was a passenger, had a tire malfunction and hit the median, according to the team.
Cordero exited the vehicle and was standing on the road's shoulder when a car driven by a 47-year-old woman smashed into the passenger side of Smith's car.
According to a Cleveland police report provided by the Browns, Cordero was transported to Fairview Hospital and pronounced dead.
Police said the other driver admitted to drinking. No charges have been filed and toxicology reports are pending.
Smith was not impaired or injured, police said.
Smith and Cordero had a daughter together last month. Cordero was 26.
The Browns called a team meeting later Wednesday morning to tell the players.
"Words cannot describe the sorrow we feel for Chris following the loss of his girlfriend, Petara," Browns owners Dee and Jimmy Haslam said in a statement. "Our entire organization mourns with Chris, his family and the Cordero family. We will do everything possible to offer them our support, comfort and any resources in this most difficult time."
Information from The Associated Press was used in this report.