White Sox manager Ozzie Guillen was suspended two games and Royals manager Trey Hillman was given one game. All four penalties also included undisclosed fines.
Olivo and Greinke appealed their suspensions, which were to begin with Tuesday night's game against Boston.
RED SOX: A fan of the team sued the New York Yankees and two of its fans, alleging he was attacked at Yankee Stadium last summer.
In a suit filed in Manhattan federal court, Charles Hillios said he was harassed by two Yankees fans who objected to him cheering for the Red Sox last Aug. 29.
MARINERS: Optioned right-hander Brandon Morrow to Triple-A Tacoma, starting the process of converting the first-round draft pick to a starter. The team also designated infielder-designated hitter Jose Vidro for assignment.
RAYS: Recalled shortstop Ben Zobrist from Triple-A Durham and optioned designated hitter-outfielder Jonny Gomes to the International League club.
BREWERS: First baseman Prince Fielder apologized for pushing a teammate in the dugout during a loss, saying he should have done a better job of handling frustration due in part to the team's losing streak.
Fielder exchanged words and twice shoved Manny Parra after the pitcher was removed for a pinch hitter in the seventh inning of a 6-3 loss to Cincinnati on Monday night.
METS: Closer Billy Wagner was placed on the 15-day disabled list with a strained left forearm.
CUBS: Closer Kerry Wood was activated from the DL after a blister on his right index finger healed. The club also designated lefty reliever Scott Eyre for assignment.
CARDINALS: Pitcher Adam Wainwright threw 35 pitches in a simulated game and will begin what he hopes is a short rehab stint later this week.
PIRATES: Recalled right-hander Romulo Sanchez from Triple-A Indianapolis and optioned right-hander Yoslan Herrera to Double-A Altoona.
ROCKIES: Would not confirm a report that the team had claimed starter Livan Hernandez on trade waivers.