Martian Museum of Terrestrial Art, Barbican Art Gallery, London

Little green men turned this earthling's face pink: Its 'Star Trek' cum 'Kaleidoscope' aura is embarrassing, but if the aliens really had landed they'd probably enjoy this pretty good show

You might think that curating an exhibition of contemporary art from the point of view of little green men would be a toe-curling thing to do, and you would be right. The Barbican Art Gallery's Martian Museum of Terrestrial Art does just that, and it is deeply embarrassing. But it isn't as embarrassing as it is puzzling, because – the interplanetary conceit apart – MMTA is actually rather a good show. So why dress it up as a cross between Kaleidoscope and Star Trek? I'm still scratching my head over that one.

According to the show's catalogue, "The Museum was founded by the General Secretary of the Alien Affairs Committee three cycles ago, or just over a decade in terrestrial time". Don't blame me, I'm only a critic. Its rooms, broken down into themes of Kinship and Descent, Magic and Belief and Ritual and Communication, approach art as though trying to explain it to people from another planet. Put a different way, they consider it anthropologically, pondering modern Western art-making much as Claude Lévi-Strauss looked at the art of the Bororo Indians.

If the Barbican really wanted to go down the theme-park route, in other words, it could have shown the work of the many artists involved as if in an ethnographic museum, perhaps with a holographic Frenchman in a black turtle-neck hacking his way through the thickets of Hoxton. It would hardly have been sillier than bringing in extra-terrestrials, and might have reminded one less of an ad for powdered mash.

Still, the Martian Museum's anthropological approach does intrigue on various levels. For all the weakness of its running gag, the show draws interesting parallels between familial and artistic cults of ancestry. Putting Sherrie Levine's after-Duchamp urinal, Fountain (Buddha), in the broad context of inheritance makes you see it again in quite a different way. Putting it next to Tacita Dean's sound piece, Looking for the Spiral Jetty – a homage to the mythical land artist, Robert Smithson – makes you wonder if contemporary art-making isn't really just the latest act in a timeless drama of ancestor-worship. Dean's wistful last words – "I'm not sure this is the Spiral Jetty" – sum up our era nicely: a time of lost fathers and lost gods, of journeys without end.

Formally, too, MMTA's pseudo aliens have a talent for making gratifyingly off-the-wall connections. What links Thomas Hirschhorn's Musée Précaire Albinet – an outsized Bic lighter stuck with pictures of Duchamp, Mondrian and Andy Warhol – with Tatiana Echeverri Fernandez's Fraulein Antoinette, Brian Jungen's 2000, and Isa Genzken's Untitled (1998)? For the purposes of this show at least, these deeply different works are all totems, a claim that seems ridiculous until you see them side-by-side.

Genzken's sculpture may be small and made of wood and mirrors, Fernandez's ceramic and etiolated and Jungen's vast and built of golf bags, but they are all noticeably vertical. Since their common subject is, roughly speaking, the capitalist cult of commodity, this similarity seems more than coincidental. It also seems unconscious. While Jungen's golf-bag monolith clearly sets out to play at menhirs, the other works are tall because that is how fetish-objects have always ended up. This in itself is something of a revelation, suggesting that contemporary art is not the all-new thing its propagandists would have us believe.

All of which is to say that the Martian Museum of Terrestrial Art is full of challenges and surprises, and also full of art: I gave up counting the names listed between Marina Abramovic and Cerith Wyn Evans, but there must be getting on for a hundred. Thanks to the kookiness of MMTA's thinking, many of these artists are represented by works from untypical moments in their careers. Who remembered Mona Hatoum making baskets, or Yves Klein's momentary lapse into red? And if there are occasional moments of silliness – Damien Hirst's Isolated Elements Swimming in the Same Direction for the Purpose of Understanding really shouldn't have been included under "Traps" – they are outnumbered by clever connections and visual puns.

So why the Martians? I can only think that we owe them to that weasel word "accessibility" – that if MMTA's curators had tried to sell their show as a serious exercise in the anthropology of art, people would have stayed away in droves and the Barbican would have lost brownie points at the Department for Culture, Media and Sport. Which is a shame, because it is quite possible to come out of this exhibition thinking it has all been a bit of a joke, when it is actually deeply serious and rather clever.

Barbican Art Gallery, London EC2 (020 7638 4141) to 18 May