On Saturday, Escobar had the slur "maricon" written on his eye black as the Blue Jays took on the Boston Red Sox. Under his right eye were the words "tu ere," while "maricon" was etched under his left eye, according to the Daily Mail.
Toronto said it would do its own investigation of the slur in a statement released Monday.
"The Toronto Blue Jays do not support discrimination of any kind nor condone the message displayed by Yunel Escobar during Saturday's game," the organization said, according to MLB.com's AJ Cassavell. "The club takes this situation seriously and is investigating the matter."
Writing on eye black is common among professional athletes, although most of the messages are Bible passages or other non-controversial phrases.
Players wear eye black to prevent sun glare, as reported by the Associated Press.
Escobar, 29, was expected to address the media Tuesday afternoon at Yankee Stadium before the Blue Jays square off against the New York Yankees, ESPN.com's Jerry Crasnick reported.
Blue Jays General Manager Alex Anthopoulos, manager John Farrell and coach Luis Rivera are also scheduled to be with Escobar during the media availability, according to Cassavell.
The shortstop didn't take the field Sunday, but it wasn't due to the gay slur, according to Fox News Latino. Escobar was scratched from the game because he was battling the flu.
While the words on Escobar's eye black can be taken as a gay slur, that might not have been his intention, University of Toronto Spanish professor Maria Cristina Cuervo told the Toronto Star.
"It is derogatory, but it's not necessarily homophobic," Cuervo said. "I would take it as, 'You are like a girl. You're weak.' I don't curse much, so I don't know the appropriate level in English. It has to be something like 'wuss'."
In Cuba, where Escobar is from, "maricon" is interpreted as "a slur referring to homosexuals," Cuba expert and University of Miami professor Michelle Gonzalez told the Toronto Star.
"I suppose people will use it in jest, but I don't know if that makes it any less offensive," she told the paper. "People will say many things in private. People swear. But there is a difference when you display it."