Gregg yelled at Ortiz when the Boston designated hitter hit a fly ball in the eighth inning of the Red Sox' 10-3 win last Friday. Ortiz moved toward Gregg and both players threw punches -- that didn't appear to make contact. Both benches and bullpens cleared.
In addition to the suspensions, both players were fined an undisclosed amount. Baltimore pitcher Mike Gonzalez was handed a three-game suspension and also fined for throwing at Ortiz in Sunday's game.
Baltimore Manager Buck Showalter was suspended one game.
The Gregg and Showalter suspensions, unless appealed, are to begin Thursday. Gonzalez will begin his suspension July 18, when the Orioles next play the Red Sox.
Ortiz's suspension is to start Friday. Boston is off Thursday.
Baltimore's Jim Johnson and Boston's Jarrod Saltamacchia and John Lackey were fined for their actions Saturday when there was another bench-clearing incident.