The multi-millionaire - who has Belgo restaurants in five places around the world - was told to chop onions at Belgo's in Covent Garden.
But after an earful from the head chef, Tony La Castro, he tore his microphone off and told the film crew to "stick your programme".
He later returned to complete work on the show, broadcast on Wednesday on BBC Two.
Back To The Floor takes bosses and makes them spend a few days getting their hands dirty doing the work of their normal employees.
Series producer Hugh Dane remarked: "Johnson found it tough on the shop floor.
"Perhaps the heat of the kitchen was a bit much, but he was soon back and he did learn something."
Pay and conditions
Past industry bigwigs featured on the programme have included prison service director Martin Narey.
Most have been happy to "get their hands dirty" and learn about life on the other side of the boardroom door.
Mr Johnson, 38, was asked to do shifts as a waiter, chef and front-of-house manager.
He was told off for leaving menus on the table, forgetting to give customers their bread and being too slow.
Mr Johnson's outburst was immediately preceded by the chef complaining about pay and conditions.
The former Pizza Express owner, Mr Johnson had not worked on a restaurant floor for 15 years prior to the programme.
Speaking about his behaviour, he admitted having a problem with his patience.
"Unquestionably, I became irritable but I'm not the first person to lose their temper on the show, although I may be the first to take my microphone off."
Mr Johnson also owns exclusive London restaurants The Ivy and Le Caprice.
He became chairman of the Belgo Group three years ago and is a major shareholder and is now reputed to be worth £60m.