The suspension comes after an investigation by Major League Baseball into the incident during Toronto's tension-filled 8-4 loss at Atlanta.
An MLB official said there will be no additional suspension by the league.
Pillar, 28, apologized after the game for making the comment after Atlanta Braves pitcher Jason Motte struck him out in the top of the seventh inning.
"It was immature, it was stupid, it was uncalled for," Pillar said, according to MLB.com Blue Jays reporter Gregor Chisholm. "It's part of the game, it's just, I'm a competitive guy and heat of the moment. Obviously I'm going to do whatever I've got to do to reach out and apologize and let him know he didn't do anything wrong, it was all me."
Pillar, the Blue Jays' leadoff hitter, also apologized Thursday on Twitter.
"I have apologized personally to Jason Motte, but also need to apologize to the Braves organization and their fans, and most importantly, to the LGBTQ community for the lack of respect I displayed last night," Pillar said. "This is not who I am and will use this as an opportunity to better myself."
The Blue Jays released a statement on Thursday before announcing the suspension.
"In no way is this kind of behavior accepted or tolerated, nor is it a reflection of the type of inclusive organization we strive to be," the Blue Jays said. "We would like to extend our own apologies to all fans, Major League Baseball and especially the LGBTQ community."
On Thursday, MLB Commissioner Rob Manfred was asked about the incident at the conclusion of the league's quarterly owners meetings in New York.
"We're in the process of trying to gather the facts as a prelude to determine whether and what discipline is appropriate," Manfred said. The MLB official CNN asked about the suspension said the league consulted with the team and supported the decision to suspend Pillar.
The fifth-year player is hitting .305 this season and is in the top 10 in the American League in at-bats, runs, hits and doubles.
ESPN reported the suspension will cost Pillar $6,066 in salary.
MLB punished a player for using a homophobic slur in 2012. Shortstop Yunel Escobar
, then playing for the Blue Jays, was suspended for three games after writing a homophobic slur in Spanish on his eye black, the substance ballplayers put below their eyes to reduce the sun's glare.