A police report says the 46-year-old former major leaguer was stopped by police shortly after 1 a.m. on May 30 after he made a wide right turn and was weaving within his lane.
Police say Grace didn't have his wallet or license with him at the time. They say Grace was arrested on suspicion of driving with a blood-alcohol level of more than the legal limit of 0.08 percent.
Scottsdale police spokesman Sgt. Mark Clark said Thursday afternoon that results of the blood-alcohol tests on Grace weren't available yet.
A Diamondbacks spokesman says the team had no comment on Grace's arrest, calling it a "pending legal matter."