Kelly, 62, tweeted early on Monday morning saying the virus had “finally got me” and she had returned a positive result over the weekend.
“Thanks to the vaccine it’s not too bad and I hope to be back at work very soon,” she wrote.
“Huge thanks to @carolvorders who will be hosting @lorraine until I’m back.”
Kelly did not confirm when she will return to her eponymous daytime programme.
Vorderman, 61, told viewers that Kelly had caught “the dreaded you know what” and wished her a “speedy recovery”.
The former Countdown co-host then joked: “I didn’t look like this at five o’clock this morning, that is for sure.”
Following her post, Kelly received a flurry of replies from famous friends such as Angela Rayner, Labour’s deputy leader, and ITV journalist Paul Brand, as well as fans wishing her well.