No penalty has been announced by the commissioner's office involving the 25-year-old left-hander, who is not on the Twins' 40-man major league roster. Thompson still has time to appeal.
General manager Terry Ryan said Saturday that suspension involved "recreational drug use."
Taken by the Florida Marlins with the 22nd pick on the first round of the 2005 amateur draft, Thompson made his major league debut with Pittsburgh last year, when he had a 7.04 ERA in one start and four relief appearances.
Says Ryan: "We're going to keep him. He's just suspended without pay. When you got 160 kids -- and this guy is not a kid -- there is no excuse. So we're going to take care of it. I'm disappointed in that."