Rooney arrived at St Andrew’s on October 11 on a three-and-a-half-year contract.
At the time, the club sat in sixth place in the Championship following back-to-back wins under ex-manager John Eustace.
Under Rooney, Birmingham lost nine of the 15 games they played.
It leaves the club in 20th place in the Championship table.
“Football is a results business – and I recognise they have not been at the level I wanted them to be. However, time is the most precious commodity a manager requires and I do not believe 13 weeks was sufficient to oversee the changes that were needed.
“Personally, it will take me some time to get over this setback. I have been involved in professional football, as either a player or manager, since I was 16. Now, I plan to take some time with my family as I prepare for the next opportunity in my journey as a manager,” Rooney’s statement said in part.