The punishments stem from Sunday's game against the Kansas City Royals in which it was deemed that Sanchez intentionally threw at Royals shortstop Alcides Escobar in the eighth inning of a 5-2 Toronto win.
Sanchez's efforts, which also earned him an undisclosed fine from MLB, came after two Blue Jays batters had been hit by pitches. Toronto third baseman Josh Donaldson was hit in the first inning and narrowly missed being hit two other times in the game, while shortstop Troy Tulowitzki was hit in the seventh inning.
Gibbons was ejected in the seventh after Tulowitzki was hit and Donaldson was buzzed again. In a statement, MLB said Gibbons' suspension was the result of his decision to return to the field when a scrum broke out between the two teams in the eighth inning.
The animosity between the two teams carried on after the game with Toronto slugger Jose Bautista saying he lost respect for Royals manager Ned Yost as a result of Sunday's efforts. Edinson Volquez, who plunked Donaldson, called the Blue Jays slugger "a little baby" after the game.
Not to be outdone, Royals pitcher Yordano Venturacalled Bautista a "nobody" in a series of tweets in Spanish that he later deleted. Ventura has since apologized for his angry tweets.
Gibbons will serve his suspension Tuesday night when the Blue Jays host the Minnesota Twins, while Sanchez has chosen to appeal his penalty and will be available.
Blue Jays win after Gibbons gets ejected
Baseball Tonight Spotlight: Toronto manager John Gibbons is ejected in the seventh inning after arguing with the home plate umpire, as the Blue Jays beat the Royals 5-2 to take three of four in their series.