The production, which stars Meera Syal and Paul Bhattacharjee, is running at the Noel Coward Theatre as part of the BP-sponsored World Shakespeare Festival.
According to a statement from the RSC: "Just before the second half of the RSC’s production of Much Ado About Nothing at the Noël Coward Theatre yesterday evening (23 October), two people went onto the stage to protest about BP’s sponsorship of the World Shakespeare Festival.
"They then left the auditorium and our Company Stage Manager went onto the stage to explain this was an unexpected, peaceful protest and it was the RSC’s policy to allow these to happen where appropriate and safe to do so. The performance recommenced a few minutes later."
The protesters staged a Shakespeare-inspired playlet challenging the RSC over its decision to accept sponsorship from BP. According to a statement from Reclaim Shakespeare, "the audience responded with laughter and applause."
Speaking to Whatsonstage.com, Reclaim Shakespeare's Richard Howlett said: "This protest was directed at Gregory Doran, given that he's a month into his artistic directorship. We want to know whether he's going to continue to accept the same sponsorship deal as his predecessor."
Doran, who took over from Michael Boyd at last month's AGM, said: "BP has sponsored the World Shakespeare Festival as Founding Presenting Partner, and their support has allowed many important elements of the Festival to go ahead.
"We consider our potential partners very carefully and the decision to receive sponsorship from BP was taken with the full backing of our Board."
A spokesperson from the RSC told Whatsonstage.com: "It's fine for people to protest in a peaceful fashion, but this doesn't affect our decision that we were right to accept sponsorship from BP."
Much Ado About Nothing continues at the Noel Coward until 27 October.