Al Turnbull, a former tutor, used a personal Instagram account to post a promotional photo for the university's Academic Learning Centre. It shows him standing with a woman who is seated at a table.
The caption under the Instagram image reads, "Yup that's right, I'll tutor you and check out your cleavage free of charge," followed by the hashtags "awkward" and "powerstance."
Turnbull told CBC News the image was posted months ago, before he was elected president of the students' union.
"It's not surprising at all that this is coming out now. It has surfaced at the time. It's something I had already apologized for," he said, adding that the post has been removed.
Turnbull's Instagram image was recently reposted on a Tumblr blog, and the caption has outraged local anti-harassment advocates like Jodie Layne of Hollaback Winnipeg.
"That is street harassment, and that is not OK," she said.
"Whether it's being serious about it or making light of it, it's not a funny situation for women that it happens to, so it's really angering and frustrating."
Turnbull said he believes his critics have reposted the photo in a bid to ruin his character.