The woman grandmaster title is only for women and requires a lower rating of 2,300.
The commentators were discussing whether Zhu Jiner could become grandmaster, when Mr Smirin said: "She's a woman grandmaster or what?... Why she wants to be like men grandmaster in this case?"
Mr Smirin went on to appear to admit that he had privately said "chess is maybe not for women".
Fellow commentator Fiona Steil-Antoni said to him: "You're saying, you know, 'chess is maybe not for women'," and Mr Smirin replied: "I didn't say it openly... in private, private conversation."
And he also seemed to admit saying another female player - Grandmaster Aleksandra Goryachkin - had been "playing like a man".
"That's true," said Mr Smirin, when questioned about his apparent comments. "She played in Russia super final. Small minus she made, but it was very strong tournament. She also had like 2,600 plus rating."
Challenging him again, Ms Steil-Antoni asked: "What does that have to do with playing like a man, only men can play well?"
"No, no," Mr Smirin responded. "But she's playing in style, positional style... But OK, I'm always curious, why can women play among men but men cannot play with women in women tournaments? Interesting question."