After hitting a home run in the second inning off Los Angeles Dodgers pitcher Yu Darvish, Gurriel returned to the Astros dugout, where he used his fingers to motion at his own eyes in a mocking gesture and appeared to mouth a derogatory term in Spanish.
In a statement, an MLB spokesman said: "We are aware of the situation and the Commissioner intends to speak with the player tomorrow."
Speaking through an interpreter after the game, Gurriel said he made the gesture because he hasn't had success in the past against Japanese pitchers. In particular, he was 1-for-7 with one strikeout this season against Darvish.
"I did not mean it to be offensive at any point," Gurriel said. "Quite the opposite. I have always had a lot of respect [for Japanese people]. ... I've never had anything against Darvish. For me, he's always been one of the best pitchers. I never had any luck against him. If I offended him, I apologize. It was not my intention."
The 33-year-old Gurriel is a native of Cuba who played for the Yokohama DeNA Baystars of the Japanese Central League in 2014. Darvish is of Japanese and Iranian descent.
Gurriel said it's common in Cuba to use the word "chinito" to describe someone of Asian heritage, although he admitted he realizes it's considered offensive in Japan.
Darvish, also speaking through an interpreter, called the gesture and the word "disrespectful."
"I feel like, of course, Houston has Asian fans and Japanese fans, and Asian fans live all over the place," Darvish said. "And acting like that, it's just disrespectful to people around the world, to the Houston organization. It's not OK.
"Including him and I, nobody's perfect. Everybody's different. We've just got to learn from it. He made a mistake, and we've just got to learn from it. We are all human beings. It's just learn from it, and we've got to move forward."
Astros manager A.J. Hinch described Gurriel as "remorseful." Most Astros players said they weren't aware that Gurriel had made a gesture or that they hadn't seen it.
Dodgers outfielder Enrique Hernandez described the situation as "disappointing."
"It's just unfortunate that he did that right after the homer and not thinking the cameras were on him," Hernandez said. "I'll let the league handle [potential discipline]. I'm not the right guy to handle that one."
A source in the Dodgers organization said the team is "very upset" about the situation, "especially in these times in this environment."
Darvish later tweeted a statement, saying people should put effort into "learning rather than to accuse [Gurriel]."
"If we can take something from this, that is a giant step for mankind," Darvish wrote. "Since we are living in such a wonderful world, let's stay positive and move forward instead of focusing on anger. I'm counting on everyone's big love."
Darvish played professionally in Japan from 2005 to 2011 before joining the Texas Rangers in 2012. He was traded to the Dodgers at this year's July 31 trade deadline.
The Astros lead the series 2-1, with Game 4 set for Saturday at Minute Maid Park.
ESPN's Marly Rivera and Ramona Shelburne contributed to this report.