Strawberry's sport utility vehicle hit a street sign and a car while weaving through traffic outside downtown Tampa, the Hillsborough County Sheriff's Office said.
An off-duty deputy, watching through his rearview mirror, saw Strawberry "weaving all over the road,'' a news release from the sheriff's office said.
The deputy watched Strawberry's SUV veer off the roadway and hit a street sign, then come back onto the road, police said. The officer then followed him and saw him strike an Isuzu and drive on.
The deputy, driving an unmarked vehicle, flagged down Strawberry a few blocks away and held him until on-duty officers arrived.
Strawberry, 38, was held at the scene in the back of a deputy's cruiser, then taken to jail, deputies said. He was charged with leaving the scene of accident with property damage and with reckless driving. The department said testing was under way to see if he had used drugs or alcohol.
As a player for the New York Mets, Strawberry was the National League's rookie of the year in 1983 and three years later helped the team win the World Series. But he has battled alcohol and drug problems for years and was diagnosed with colon cancer in October 1998.
He was suspended for most of last season after his arrest in Tampa in April 1999 on drug and solicitation charges.
Strawberry pleaded no contest to those charges and was sentenced to probation. Then, this year, he was suspended from baseball for a year after he tested positive for cocaine in January. And last month, he underwent another round of cancer surgery.