"I am going to play tonight because it is something she would want me to do," Smith said in a statement, per Jake Trotter of ESPN. "She would want me to keep doing what I love and stay strong. I play for her tonight. She is my why."
The Browns will face the New York Jets at MetLife Stadium Monday night.
Cordero was killed Wednesday on I-90 West in Cleveland after the vehicle Smith was driving collided into the median after tire malfunction. Both passengers got out of the car without major injuries, but Cordero was struck by an oncoming vehicle and died.
Cordero also gave birth to a daughter last month, which caused Smith to miss his team's Week 2 preseason game.
"Smith will receive the full team’s support of resources and will have the opportunity to grieve as he sees best fit, including being excused from or participating in any team activities, if desired," the Browns said in a statement last week.
The 27-year-old didn't practice during the week but has decided to play in the Week 2 game.
Smith is in his second season with the Browns and sixth year in the NFL after being taken in the fifth round of the 2014 draft.