The benighted businessman was criticised by the Trade Union Congress and the Recruitment and Employment Confederation after he asked mother-of-two Katie Hopkins how she intended to care for her family if she became his apprentice.
He said to Hopkins: "How's life going to be if I say to you, 'Katie right, you're down in London. You've got to move your family, move your location?'...I'm worried here."
Hopkins eventually chose to stand down from the competition because she was reluctant to uproot her family from their Devon home.
Fellow contestant Kristina Grimes was also grilled about her family circumstances and whether she would be prepared to move to become Sugar's apprentice.
Brendan Barber of the Trade Union Congress said: "The Apprentice is just a show but had (Wednesday's episode) been a genuine interview, Kristina and Katie could have had real grounds for complaint against Sir Alan.
"Any employer who asks the only female candidates about how their children and personal circumstances may affect their ability to do their job could find themselves in hot water."
Tony Hadley, director of the Recruitment and Employment Confederation said: "It simply isn't acceptable to assume that only women have caring responsibilities in the modern world."
However, a representative for Talkback Thames, the makers of The Apprentice, insisted that Sugar's line of questioning reflected the unique nature of the opportunity he is providing, saying: "As part of the interview process, Sir Alan and his colleagues interrogated all of the candidates about their commitment to the process and the job.
"He wanted to put them under pressure to be fully confident that they were serious about the opportunity he was offering them."