Arizona Department of Public Safety officials say troopers pulled over Tomas, 27, around 9:30 a.m. Thursday.
He was booked into the downtown Phoenix jail, and his Mercedes Coupe was impounded.
Authorities say Tomas could be facing up to 30 days in jail and a fine up to $500 on the criminal speeding charge. A reckless driving charge could lead to a suspended license.
"We are very disappointed to learn of this news," the Diamondbacks said in a statement issued Thursday afternoon. "We are still gathering facts, and will refrain from further comment at this time as this is a pending legal matter."
Tomas hit 31 home runs in 140 games in 2016, but a nagging core injury limited him to 47 games last season.