The Sun revealed how 16-year-old Ben Clark approached Sugar at a cycle show at the NEC Arena, Birmingham.
The schoolboy said to Sugar, as a joke: "Alan, you're fired."
Sugar swiftly replied: "And you're a prick."
Clark, who is now 17, described his exchange with Sugar: "I saw Alan Sugar near a stall and he was looking at bikes.
"It's known that he likes bikes and that he's quite a keen cyclist himself. He seemed to have a guide there with him - along with a security entourage.
"I just said to him, 'Alan... you're fired.' He turned round and said to me, 'You're a prick'.
"There were about 30 bystanders around including children so I just let it go. His security entourage didn't react at all."
Clark admitted that he was taken aback at the multi-millionaire's reaction to his joke.
He said: "It's not right. He's a Lord and I was 16 - a Year 12 schoolboy. Also he has a TV show where he deals all the time with people of my age group.
"I was a bit shocked because I wouldn't expect him to say that in front of bystanders."