Lee failed to start his new job on Tuesday after phoning in to say he was suffering from a ‘flu-like virus’.
He apparently fell ill while on holiday in Spain with girlfriend Nicola Jellyman last week, and told bosses he was sick when he returned on Sunday.
A company spokesman said: “Lee is at home with a virus. We’ve known he’s not been well for three or four days.
“He’s frustrated that he can’t be at work because he wants to get going but he knows that he needs to be at home.”
Lee is expected to start work “in a few days”.
A show insider told The Sun: “This will make Sir Alan really cross because he hates being let down.”
But Lee denied claims that Sir Alan was not happy. “He’s certainly not furious,” he said. “People get ill and he understands that.”
Lee landed the £100,000-a-year job after beating retail buyer Claire Young in the final of the BBC1 reality show last month.
He is helping to develop digital display advertising screens at Sir Alan’s holding company Amshold in Brentwood, Essex.
The news comes after self-made multi-millionaire Sir Alan stepped down as chairman of Amstrad on Tuesday.
He will continue to be involved with his other business interests, which include Amshold, Amsprop, Amsair and Viglen computers.
Sir Alan said: “This is a move that has been planned for a while and it’s the right time for me to step down from my role at Amstrad.”