Sugar said that Shah, 35, had failed to live up to her billing as "one of Britain's best business prospects".
"You showed no initiative in spotting that you were going for a disaster," said Sugar. "And on that basis, Anita, you're fired!"
Shah was brought in the boardroom alongside senior sales consultant Debra Barr by team leader Mona Lewis, after the girls' team Ignite lost out to the boys' team Empire in a cleaning challenge.
Empire, led by Howard Ebison, made £239.61 profit compared to Ignite's £160.55.
Confronting the girls about their failure, Sir Alan said: "There are reasons why each one of you should be fired. Mona, you haven't shown me any business acumen. Anita, you were on the back of that van and you were seeing the money flow out. Debra, at the end of the day you were seriously responsible for a lot of things that went wrong on this task."
Speaking about her exit afterwards, the law graduate blamed her early departure on Sir Alan's dislike for lawyers.
"I'm bitterly disappointed but I accept that I wasn't a stellar performer, and without appearing to have a chip on my shoulder I just think that Sir Alan doesn't particularly like lawyers," she said. "Let's see in 10 years if he doesn't sit and think, 'maybe I made the wrong decision'."
The Apprentice continues next Wednesday on BBC One at 9pm.
> Click here to read our interview with Anita Shah