David Anderson said during a farm visit in southern Alberta that he has instructed his staff to remove the video link from his website.
Anderson, parliamentary secretary to the agriculture minister, said the nine-minute animated video had been around for a year without receiving any complaints.
The phrase "talking Eskimo" was used three times in the video to explain opposition to the Canadian Wheat Board by some farmers.
National Inuit Leader Mary Simon said the term is offensive to her people and has no place in public discussion.
The name "Eskimo" means "eater of raw meat" and was given to the Inuit generations ago by their rivals at the time, the Dene.
"An Ottawa reporter yesterday raised the issue that one of the statements in the ... video could offend some people," Anderson said Tuesday.
"None of us in the House of Commons, and certainly no one here either, is in the business or has any interest in offending people, and we certainly apologize to anyone that that has offended."
Anderson was on a farm near Lethbridge to talk about legislation the federal government has tabled to take away the wheat board's monopoly.
The video involved a fictional wheat board executive and a Saskatchewan wheat farmer wanting to sell his grain to a Calgary baker.
The executive tells the farmer he's "talking Eskimo" when the producer expresses concern that he can't do such a thing in Saskatchewan.