"Run Baby Run" is a single by singer Sheryl Crow from the album Tuesday Night Music Club released by A&M Records. It was originally released in 1993. It failed to chart but was a minor radio hit in several other countries. "Run Baby Run" was released for a third time after the success of "All I Wanna Do" and "Strong Enough". It reached no. 24 in the UK charts in July 1995.