Quentin charged the mound after being hit by a Greinke pitch in the Dodgers' 3-2 victory over the Padres at Petco Park.
"I was hoping for the best, but expecting the worst," Padres manager Bud Black said. "I know these things vary from case to case, and eight games seems a little on the high side."
Greinke, who suffered a fractured collarbone, was also ejected as were teammates Matt Kemp and Jerry Hairston Jr. Hairston was suspended one game. Like Quentin, Hairston will also appeal the decision.
Quentin was in the starting lineup in left field for the first game of a three-game series on Friday against the Rockies, going 0-for-4 with two strikeouts.
The Padres head to Dodger Stadium on Monday for the first of three games against the Dodgers, one of 16 more meetings between the teams this season.
"We'll miss having Carlos however long he's out, but other guys have to keep the offense going while he's not in the lineup," Padres first baseman Yonder Alonso said.
Joe Garagiola Jr., senior vice president of standards and on-field operations for Major League Baseball, made the announcement on Friday.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.