Party leader Ed Milliband said remarks Ahmed made in a television interview in Pakistan were "disgraceful," The Independent reported.
"There's no place for anti-Semitism in the Labor Party, and frankly anybody who makes those kinds of comments cannot be either a Labor lord or a Labor member of Parliament," Milliband, who is Jewish, said.
Ahmed, born in Pakistan, was named to the House of Lords by former Prime Minister Tony Blair. In 2009, he pleaded guilty to dangerous driving and was sentenced to 12 weeks in prison with police presenting evidence he sent long text messages before a fatal crash.
In the interview, Ahmed blamed Jewish news media owners for his imprisonment. The interview was broadcast in Pakistan last April but only became public in Britain when The Times of London published it on its website this week.