The Project Runway host and her bodyguard lover were dining at New York City eatery The Spotted Pig with a friend when things turned sour and Heidi is said to have abruptly left the restaurant.
A source told the New York Post newspaper: "They had been drinking with a male friend at a table, and things became heated very quickly."
The 40-year-old supermodel - who has four children, Leni, eight, Henry, seven, Johan, six, and Lou, three, with ex-husband Seal - attempted to hail a taxi, but when she couldn't get a ride home, returned to the restaurant but "refused" to rejoin Martin and the couple's pal.
'She'd had one drink too many'
Heidi "stood in the doorway looking upset", prompting her burly South African boyfriend to go outside and speak to
However, after another heated exchange, Martin left the restaurant and Heidi returned to the table to dine with her friend.
An insider close to the Germany's Next Top Model star added: "She'd had one drink too many and they had an argument. All couples have disagreements, but most don't get recognised when they have them."
Heidi began dating Martin last year after hiring the bodyguard to look after her four children following her split from Seal.
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South AfricaCommunicate Cape Town ITR24000 - R27000
HousesR 9 000 000
FarmsR 2 750 000
HousesR 2 150 000