In photographs published in a newspaper, Saatchi embroiled in a violent dispute with Lawson while sitting outside Scott's in Mayfair, central London. He was pictured to lean over and grab his wife by the throat, reported Daily Mirror.
Lawson, 53, looked terrified before leaving the restaurant alone in tears. Onlookers claimed Lawson dabbed her eyes on a napkin as her husband tapped his cigarettes on the table.
She is then said to have downed her glass of red wine before beginning to speak in a trembling voice, placing a hand on his left wrist on the table.
"It was utterly shocking to watch. I have no doubt she was scared. It was horrific, really. She was very tearful and was constantly dabbing her eyes. Nigella was very, very upset. She had a real look of fear on her face," said an onlooker.
According to reports, no complaint was believed to have been made about the incident and no investigation had been launched.
The couple, who have both been married before, are due to celebrate their 10th anniversary in September.