Kennedy's suspension is the longest handled out by the league for on-field conduct since Chicago Cubs catcher Michael Barrett was handed a 10-game suspension for an incident with White Sox catcher A.J. Pierzynski on May 20, 2006.
Kennedy is appealing the decision, pointing to his track record as proof he's not a troublemaker.
"Ten games, I think they're trying to set an example," he said before Arizona's game in San Diego on Friday night.
Hinske is also appealing and put most of the blame on Dodger rookie Yaisel Puig, who was right in the middle of things but only received a fine.
"I've been a model citizen in this league for 12 years," Hinske said. "And then there's Puig, who's been in the league for 12 days and he gets no games. So you tell me what's right."
Belisario served a one-game suspension on Friday night for "aggressive actions" while Dodgers reliever J.P. Howell and infielder Skip Schumaker appealed the two-game suspensions they received from MLB Senior Vice President Joe Garagiola Jr.
Los Angeles manager Don Mattingly and Arizona's Kirk Gibson were given one-game bans, while Dodgers hitting coach Mark McGwire must sit two games.
Bench coach Trey Hillman filled in for Mattingly on Friday night when Los Angeles played at Pittsburgh while Arizona bench coach Alan Trammell took over for Gibson in San Diego.
Garagiola cited Kennedy for intentionally throwing a pitch at the head of Zack Greinke after a warning had been issued and Hinske for leaving the dugout and his "aggressive actions."