Meanwhile, it was also announced that Rowan Atkinson, who is starring as Fagin in Oliver!, will be out of action for a few weeks while he recovers from hernia surgery.
Horne, who is starring in Entertaining Mr Sloane at the Trafalgar Studios theatre, fell to the floor 15 minutes into the second half of yesterday's matinee show.
He was treated on stage before the manager asked the audience to leave.
Horne's publicist said the Gavin And Stacey star, who has also been starring in a sketch show and a film recently, had been suffering from "the effects of having worked flat-out".
Horne spent about an hour in hospital yesterday and was recovering at home today, the publicist said.
It was not yet known when he will return to the stage.
His co-star in Entertaining Mr Sloane, Imelda Staunton, also pulled out of the performance after becoming unwell and understudies last night replaced the two leading lights in the play written in the 1960s by Joe Orton.
Meanwhile, those behind the hit West End show Oliver! announced that Russ Abbot will stand in for Atkinson while he recovers from surgery for an indirect inguinal hernia.
Doctors are confident that he will be well enough to return to his role of Fagin on 27 April, following a three-week recovery period.
A statement from the show said: "Rowan has been nursing the problem for a few weeks but it flared up badly whilst on a break with his family this week.
"He has cut short his holiday to fly back to have surgery immediately to speed the recovery process.
"The condition, whilst neither serious nor dangerous, is extremely painful and prevents normal movement, making performing impossible."
Abbot will return to the part of Fagin at the Theatre Royal, Drury Lane, for two weeks from 13 April.
Tim Laurenti, who was scheduled to play Fagin during Atkinson's holiday, will continue playing the role until 11 April.Reuse content