Several pictures posted online show Escobar with the message written on his eye-black, a sticky tape worn under players' eyes to reduce glare from the sun and stadium lights.
The words under the 29-year-old Cuban's eyes were "TU ERE MARICON," which can be translated as "You are a fa--ot."
Blue Jays general manager Alex Anthopoulos has scheduled a media conference to address the issue Tuesday afternoon in New York, where the team opens a three-game series at Yankee Stadium.
Escobar, manager John Farrell and coach Luis Rivera are also expected to attend.
"The Toronto Blue Jays do not support discrimination of any kind nor condone the message displayed by Yunel Escobar during Saturday’s game," the statement said. "The club takes this situation seriously and is investigating the matter."
MLB spokesman Pat Courtney also confirmed the commissioner's office is investigating the incident.
'This is a bad word'
It would seem the phrase on Escobar's eye-black went virtually unnoticed until season-ticket holder James Greenhalgh posted a photograph online.
Greenhalgh sits near the dugout and often takes photos of players that he uploads to Flickr.
Accompanying this particular closeup is a lengthy explanation of Greenhalgh's reservations about posting it in the first place, and his musings as to Escobar's motive.
"This is a bad word" Greenhalgh wrote of Flickr. "It's a homophobic slur.
"It may have made a closeted Blue Jay/Red Sox very upset inside. There are a million insults he could have used that would have been funny, this was not one of them."
Some Spanish-speaking people have said since the incident that the phrase is sometimes used, particularly by men, in a joking way — not in a literal way intended to insult.
Greenhalgh later tweeted a link to the closeup photo of Escobar on his Twitter account @james_in_to.
He also tweeted a link to a previous photo of Escobar with the word "Chilling" on his eye-black, to suggest that the shortstop often writes "funny stuff."
"I like Yunel a lot," Greenhalgh wrote. "He's the one who pays me the most notice when I'm at the games.
"He points to his fans, tips his cap and recognizes the support he is given. This was a mistake I hope he learns and he will never make again."
The photos stirred up controversy on Twitter and several sports blogs Monday afternoon and Escobar was trending on Twitter by early evening.
The Blue Jays open a three-game series Tuesday against the Yankees in New York.