Lawrie was also fined an undisclosed amount but has decided to appeal the decision, and there was no immediate word on when a hearing would take place.
The disciplinary action taken by Major League Baseball was in response to Lawrie tossing his helmet in the direction of Miller after disputing a strike 3 call.
"Obviously, we're going to appeal it," Lawrie said before Wednesday's game against the Yankees. "I feel that I have the right to explain my side of the story about what happened last night. I just have to suck it up, appeal it and worry about baseball, worry about playing today and getting a win."
The incident occurred with the Blue Jays trailing by one in the bottom of the ninth and one out. Lawrie got ahead in the count, 3-1, against Rays closer Fernando Rodney and was seemingly one pitch away from reaching base as the tying run.
Rodney proceeded to strike out Lawrie on a pair of pitches that clearly appeared to miss the strike zone. Lawrie immediately confronted Miller and while doing so spiked his helmet into the ground, and the helmet bounced up and hit Miller on his right hip.
"The only thing I regret is the helmet hitting him," Lawrie said. "I never meant to do that, and it shows. I threw it off the ground, it took a bad hop and it hit him totally by accident. I never meant to throw it at him.
"As that's coming across, it seems like a lot of people are saying that I threw it at him. I never threw it at him. I never had any intentions of hurting anybody. I was just frustrated at the play at the time, and that's baseball for you."
Lawrie has become a fan favorite in Toronto thanks in large part to the passion and energy he brings to the field on an everyday basis. It's that same brand of high-strung competitiveness that ultimately led the second-year player to lose his cool during Tuesday's pressure-packed ninth inning.
Toronto general manager Alex Anthopoulos has often fielded questions about whether Lawrie's style of play rubs opposing players the wrong way. On Wednesday afternoon, Anthopoulos found himself answering similar questions, but this time, they were about how Lawrie's response will affect his future relationships with umpires across the league.
"We've seen some of the great players in the game get upset," Anthopoulos said in Lawrie's defense. "This is not the first time this has ever happened. He bounced his helmet on the ground, and it happened to come up on the legs. Everyone knows that; it's there to see. It's not like you're recounting a story over the phone of, 'You won't believe what happened.'
"If he had thrown the helmet a little bit to the right or left, we're not having this conversation today. It's just, he got upset, it was a tight game, a hard loss -- all that kind of stuff."
Lawrie will now appeal the league's decision in hopes of getting the suspension reduced. The Blue Jays are not set to visit New York until the middle of July, which means the process will likely play out over a video teleconference instead of an in-person meeting at the Commissioner's Office in New York.
Anthopoulos didn't necessarily take issue with the number of games Lawrie's scheduled to miss, but he did feel an appeal was necessary to gain a better understanding of why the league decided four was an appropriate number.
The hearing will allow both sides to present an argument, and a final decision will then be announced by the league. It's not something Anthopoulos was expecting to deal with this season, but in some ways, he's still looking forward to the process.
"I just would like to maybe hear the consideration of why four," Anthopoulos said. "If someone explains that, 'Look, four is the right amount,' Brett will be the first one to say it's the right amount. We'll have to hear exactly what went into it and why four, from their side, is the right amount. Maybe it isn't. I'm not sure. I haven't really studied all the suspensions and appeals.
"We respect the process. We respect what the league has to deal with. Everyone is trying to do what they think is fair. We'll just see how it goes."
Lawrie, who was acquired from Milwaukee in December 2010 for right-hander Shaun Marcum, said he intends to speak with Miller prior to Wednesday night's game. Miller was slated for third-base duties, which should provide an opportunity to hash out any potential hard feelings.
After that, Lawrie hopes everything goes back to business as usual until his appeal is complete.
"It's part of the game; these sort of things happen," Lawrie said. "It was over as soon as I got out of the dugout. I woke up today with a smile on my face and looking forward to trying to get a win against the Yankees today."