Rodriguez was penalized for throwing at and hitting Chuck Knoblauch with a pitch in the ninth inning of New York's 11-8 win Friday night, for using obscene language and for fighting.
After hitting Knoblauch, Frankie Rodriguez was ejected. He then started yelling at the Yankees in their dugout.
The benches and bullpens emptied with some of the Yankees intent to get Rodriguez, and the pitcher knocked down Joe Girardi with two punches.
Girardi and Yankees coach Don Zimmer also were ejected following the fight. Yankees manager Joe Torre was ejected an inning earlier for arguing a call.
Grimsley's suspension is due to start Tuesday, and Rodriguez's following the five-game suspension of Mariners pitcher Jose Paniagua, who on Monday dropped the appeal of his penalty. Paniagua was suspended following a July 11 fight against the Los Angeles Dodgers.
It was not immediately known if Rodriguez and Grimsley will appeal. If they do, the suspensions can't begin until after a hearing before AL president Gene Budig.
Rodriguez and Grimsley also were fined.
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