The event, called The Worst Fucking Idea I've Ever Heard In My Life, will be held on 1 March, and ticket sales will raise money for Comic Relief.
The show, which will take place at the Apollo Theatre in London's Victoria, will be interrupted with ad breaks for Leo Burnett clients including Procter & Gamble, McDonald's, Kellogg's, Scottish Widows and Heinz.
The show's dialogue and songs have also been rewritten to incorporate product placement for these clients.
Jim Thornton, Leo Burnett's executive creative director, said: "This is something I've always wanted to do but, whenever I've mentioned it, people have said it's the worst fucking idea they've ever heard, hence the name of the project.
"It'll be either a complete success or an utter disaster but we spend our lives telling clients to take risks and to stand out from their competitors and we're really going to be doing this."
Leo Burnett is keen to develop the idea of live advertising further if it is successful. Thornton adds: "In our never-ending quest for originality, live advertising may be viable. There are practical considerations with theatre - audiences tend to be in the bar in the interval, for example - but it's an interesting medium."