Lawrie threw his helmet down in anger in the ninth inning of Tuesday's game against the Tampa Bay Rays after Miller called a strike on a 3-1 pitch from closer Fernando Rodney that appeared well out of the strike zone.
The helmet ricocheted off the ground and hit Miller's leg during the argument. Blue Jays Manager John Farrell needed to separate Lawrie from the umpire.
Farrell, too, was ejected during the incident.
Rodney went on to save the Rays' 4-3 victory over Toronto.
Lawrie was scheduled to play for Toronto in Wednesday's game against the New York Yankees as he appeals the suspension, the Blue Jays said.