The reports also indicated that Odor will appeal the punishment.
During Sunday's Rangers-Blue Jays game in Arlington, Texas, Bautista slid hard at second base into Odor's legs in the eighth inning of the Rangers' 7-6 win. Odor shoved Bautista and then landed a direct punch flush to the Blue Jay's head.
Bautista had reached base after being hit by a pitch from Matt Bush but was called out at second base on his steal attempt after violating the new rules in place this season to avoid injuries on similar plays. Odor said afterward that he didn't regret his actions.
A scuffle broke out on the field among players from both teams as Bautista and Odor tangled. There was no immediate word on whether other fines and suspensions might be handed down in the fallout.
Bautista, Odor, Blue Jays third baseman Josh Donaldson and Rangers bench coach Steve Buechele were ejected in the eighth inning.
Once calm was restored about 10 minutes later, the game resumed and Blue Jays reliever Jesse Chavez hit Texas' Price Fielder with a pitch and both benches emptied again.