There will be the piece of paper that an artist stared at for 1,000 hours over a period of five years, as well as evidence of the movie that was shot without film in the camera. "It is not a joke," stressed the Hayward Gallery's director, Ralph Rugoff, as he announced details of a summer show devoted to invisible art. "This is the best exhibition you'll never see."

The Hayward said it was staging the UK's first exhibition of art that explores invisibility and emptiness, with around 50 works by artists including Yves Klein, Andy Warhol, Yoko Ono and Maurizio Cattelan.

Inevitably, that means there will be lots of art for visitors not to see, including invisible ink drawings by Gianni Motti and a plinth where Warhol briefly stood before stepping off and leaving nothing but traces of his celebrity awesomeness. "It leaves so much up to your imagination," said Rugoff. "It's sort of like the power of radio compared to television – in great radio drama you're inventing characters in your head. There is a lot of invisible art out there, there is a lot of art you're never going to see."

Klein, perhaps the first artist to explore the subject, in 1958 staged the first exhibition completely devoid of visible content.

In talking about the show that he has curated, Rugoff drew comparisons with John Cage's silent music piece 4'33", which in turn was inspired by a young Robert Rauschenberg spending a month erasing an artwork by Willem de Kooning. "In music you only have one person do a piece of silent music but somehow in art, artists have kept coming back to the subject and are always loading different content on to the idea of invisibility or emptiness."

One room in the show will have four walls with apparently blank pieces of paper on them, but Rugoff said visitors would have a different experience with each piece.

One will be labelled Erased Playboy Centrefold because, with a nod to Rauschenberg, artist Tom Friedman spent a week with his rubbers, painstakingly removing all traces of the pin-up. "This idea of maybe by unmaking something you can make something is one of the paradoxes of invisible art," said Rugoff. "But there are things that are quite conceptual and sublime."

Included in that category is a work by Robert Barry in which he released different noble gases into the atmosphere at different places in California, taking a photograph of the empty canister and the gas.

There will be much that should provoke laughter, not least a work poking fun at the absurdity of bureaucracy that consists of a police report investigating the claim – taken seriously – by Cattelan that an invisible artwork had been stolen from the back of his car. Then there is the movie Jay Chung took over two years to make with no film in the camera – funny for some, perhaps less so for the actors.

A far more serious exhibit will be a piece by Teresa Margolles in which she takes water that has been used to wash the bodies of murder victims in Mexico City's morgue and uses it in a humidifier. Visitors walk through a room just aware of this superfine mist and its relationship to people mainly killed by drug cartels. "We see photographs all the time but this is much more intimate," said Rugoff. "You feel it on your skin."

• Invisible: Art about the Unseen, 1957-2012 will be at the Hayward Gallery from 12 June until 5 August.