The St. Lucie County Sheriff's Office said Cabrera, arrested late Wednesday, was released on bond Thursday morning, the Detroit Free Press reported.
Officers spotted a car Cabrera was driving on the side of the road and found Cabrera with an odor of alcohol on his breath, bloodshot eyes and heavily slurred speech, police alleged.
Deputies reported Cabrera said, "Do you know who I am, you don't know anything about my problems," and then picked up a bottle of Scotch whiskey and started drinking, an arrest report said.
When asked to get into a patrol vehicle, Cabrera cursed and resisted, police said.
Tigers second baseman Carlos Guillen, when asked about the affect the arrest might have on the team, told the Free Press: "Everybody is in shock. You've got to keep looking forward."
Police were called to Cabrera's home in October 2009 after he allegedly got into a fight with his wife. Three months later he entered an alcohol abuse treatment center.
Cabrera has played eight seasons in the major leagues with a career batting average of .313 with 247 home runs and 879 RBI. He has played 1,190 games with Florida and Detroit and earned $20 million last season.