"We want our players to be aware of the short- and long-term dangers of these substances."
Shapiro announced Betancourt's suspension after the clubhouse had closed before the start of their Friday night game with the Yankees. Players, including union representative Jody Gerut, were unavailable for comment.
Before going on the DL last Sunday, Betancourt had appeared in 29 games for the Tribe, and had a 2-2 record with a 2.21 ERA.
Since the policy went into effect, Betancourt would be the third Major League player to test positive for steroids or performance-enhancing drugs. (The others are Twins reliever Juan Rincon and Devil Rays outfielder Alex Sanchez.)
In a written statement, Betancourt, who will lose 10 days' pay, vowed to appeal the suspension.
"I am very angry and disappointed with Major League Baseball's decision to suspend me," Betancourt said in his statement. "I am going to file a grievance to clear my name. I am very sorry if this has caused any embarrassment and I apologize to my family, the Cleveland Indians organization, my teammates and all the fans.
"I look forward to resolving this matter and returning to the Indians as soon as possible."
Commissioner Bud Selig and the 30 team owners have gone on record as saying that they want to root steroids from the sport. Selig has pushed for tougher penalties, even for first-time offenders like Betancourt.
Selig has proposed a 50-game suspension for the first offense, 100 games for a second offense and a lifetime ban for a third.
Under his proposal, amphetamines would also be on the testing list, and players would be subject to increased random testing. An independent party would be hired to oversee the entire drug-testing program.
"Both [at] the executive council and at the meeting of the 30 clubs, everyone felt very strongly about this," Selig previously told MLB.com. "They wanted to show that in this particular group, there never has been equivocation and there isn't now. We had a very long and detailed discussion. And out of it came the resolution, first passed by the council and then the clubs."
Union chief Donald Fehr has said that the union would be willing to talk about the proposal.