Kelly Osbourne was filming her television show Fashion Police in front of a full studio audience when she turned to Melissa Rivers - daughter of comedian Joan - and said "I don't feel good", according to celebrity website TMZ.
The daughter of Sharon and Ozzy then reportedly fell out of her chair before the seizure begun.
An audience member, believed to be an emergency responder, ran up to help Ms Osbourne.
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The Home Secretary said the Government is "against cliff edges" and immigration figures will not suddenly fall when the UK leaves the EU.
Peter Whittle has said it was probably too early for Paul Nuttall to run as an MP for the party after only just becoming its leader.