The Rays contend Cabrera punched third baseman Evan Longoria during Wednesday's pileup.
"I didn't hit nobody," Cabrera said Saturday, speaking through a translator. "I don't know what it's coming from. I just come to play baseball."
Yankees first baseman Shelley Duncan, also suspended three games, said he has not decided if he will appeal.
Bob Watson, baseball's vice president for discipline, cited Duncan for "violent and reckless actions, which incited the bench-clearing incident." He penalized Cabrera for "violent and aggressive actions."
The suspensions, unless appealed, will start at the beginning of the regular season.
Trouble between the teams brewed last weekend when the Rays' Elliot Johnson crashed into Yankees catcher Francisco Cervelli.
Duncan took exception to the collision and responded four days later with a hard slide into Rays second baseman Akinori Iwamura. Tampa Bay manager Joe Maddon called the play "borderline criminal."
Cervelli broke his right wrist and a pin was inserted Wednesday. He is expected to miss eight to 10 weeks.