Scottsdale, Ariz., police said Grace, who is currently a Diamondbacks broadcaster for Fox Sports Arizona, was pulled over shortly after 1 a.m., May 30, The Arizona Republic reported.
Authorities said Grace, 46, was pulled over for allegedly making a wide right turn and weaving within his lane, and admitted having had "a few drinks."
The former first baseman was taken to a police command post where his blood was drawn. The results were still pending.
"It's a pending legal matter, and we have no comment at this time," Diamondbacks Vice President of Communications Shaun Rachau told the newspaper.
Grace, who compiled a lifetime .303 batting average, 173 homers and 1,146 RBI in 16 years for the Cubs and the Diamondbacks, was a member of Arizona's 2001 World Series Championship team.