The Jewish candidate, who is from Portsmouth but now lives in Birmingham, was called into the boardroom after a disastrous effort by the girls’ team.
For the second task of the series, the teams were sent to Heathrow Airport and told to devise and market a new beach accessory.
Apollo came up with a bookstand for use while sunbathing.
Ms Stefanicki, a self-proclaimed “PR guru”, was blamed for not speaking up about the product, which received no sales offers - a record for the programme.
During the show, she said: "I'm not keen on the product. I think the prototype is disappointing."
The 31-year-old, who has visited Israel many times and has even considered making aliyah, told Lord Sugar: "I didn't buy into it as a bookstand, but I supported the team."
Lord Sugar fired her and said: "I haven't seen anything from you."
The boys’ team, Synergy, came up with the "Cuuli", a beach towel and pillow with space to store a bottle of water.
Ms Stefanicki was not the only Apprentice to leave the show. Raleigh Addington quit because his brother was injured in an explosion in Afghanistan.