The 27-year-old agitator caught defenseman Adam McQuaid with an errant elbow to the head in the second period, drawing the ire of the outspoken bench boss.
"Suspendable. Ridiculously suspendable," Tortorella said after the game, according to The Athletic's Aaron Portzline.
Shaw was handed a two-minute minor for interference on the play:
McQuaid, who has a history of concussions, did not return to the game.
Shaw has been suspended three times over his eight-year career, most recently in 2016 when he received a three-game ban for boarding.
With two points on the night, the Blue Jackets now occupy the final wild-card berth in the Eastern Conference with five games remaining.