Nimoy wore the blue uniform while playing Mr Spock in the second season of the sci-fi series in 1967 and 68.
The costume is being put up for sale by an unnamed British fan, just months after Nimoy died at the age of 83.
It will be included in an auction of television and film memorabilia in London in September.
Other items up for sale will include a model starship used in Star Trek: The Next Generation and Deep Space Nine (above) and a stormtrooper Helmet from Star Wars: The Empire Strikes Back (below right). Both have been valued at £40,000-£60,000.
A costume (above left) worn by Superman actor Christopher Reeve for an underwater scene in the original 1978 film is expected to fetch £25,000-£30,000.
Also on offer is the The Witch King's Dagger from Lord of the Rings: The Fellowship of the Ring (above left), which is priced at £25,000-£30,000.
Arnold Schwarzenegger's jacket from Terminator 3: Rise of the Machines (above centre) is valued at £4,000-£6,000, while a set of claws worn by Hugh Jackman while playing Wolverine in X2: X-Men United is expected to fetch the same price.
The items will be among 450 lots to be auctioned by The Prop Store and Odeon at the BFI Imax on 23 September.
A costume worn by actor Leonard Nimoy in Star Trek is expected to fetch up to £70,000 when it goes up for auction in September.