Chrissy Teigen said her “heart stopped” after Donald Trump labelled her “filthy mouthed” on Twitter.
The TV presenter and her husband John Legend are frequent critics of the president, who responded in a row over criminal justice reform.
Mr Trump criticised Legend after he appeared on a TV special on the subject and said he had not been given enough credit for signing a law introducing reforms.
The president tagged “boring musician” Legend in a post to his 64 million Twitter followers and referred to Teigen as “his filthy mouthed wife”.
Teigen appeared on The Ellen DeGeneres Show and said the tweet made her “really angry”.
She said: “My heart stopped because at that moment you know that you’re about to get just the wildest group of people ever.
“It was a weird feeling. I was really angry. I think my eyes filled up with water just at the shock of it. I can’t believe this really happened right now.”
Teigen, known for her comedic presence on social media, joked: “Those two things are true. John is boring. I do have a filthy mouth.”
The Lip Sync Battle host is blocked by Mr Trump on Twitter and said she found out about the tweet from friends.
“When the card lands on you that day, it’s like, ‘Oh crap,’ because your whole night’s ruined,” she said.
“We spent the entire rest of the night, just sitting next to each other, handing each other our phone. ‘Should I say this?’ ‘No.’ ‘ Should I say this?’ ‘No, it has to be funnier. No, we’re mad! Yeah, we’re mad!’”
Teigen eventually responded by calling Mr Trump a “pussy ass bitch”, which began trending on Twitter.
“We’re still working on how to copyright the right term,” she joked.