Heidi Klum Leaves 'AGT' Taping After Feeling Ill

'AGT' is having a rough go today -- first Howie Mandel shows up to set in a full hazmat suit ... and then we learned Heidi Klum was too ill to work.

Heidi showed up to shoot "America's Got Talent" in Pasadena Tuesday with a smile, but looks can be deceiving. She felt physically ill.

Only 3 judges entered the stage -- Heidi was missing. The judges told the audience she had a case of suspected food poisoning, and Sofia Vergara joked she had sent Heidi food last night. We've learned it was NOT food poisoning -- she just felt like crap.

Unclear what's ailing her, but people get sick all the time and it has nothing to do with the coronavirus.

Interesting ... there was a full audience for the taping today. TMZ broke the story, "Jeopardy!" and "Wheel of Fortune" are now taping without an audience. Ditto for Wendy Williams and Dr. Phil's shows.

No word if Heidi's gonna dress like Howie the next time she arrives on set ...