The Tinbergen Building, which houses the departments of zoology and experimental psychology, will be closed from Monday.
A university spokesman said it was not believed there was a health risk to regular users of the building.
He said asbestos was found last year, but it was not in "accessible" areas.
A total of 750 staff are based in the building and it is used by 900 students.
A statement said: "We do not believe there is, or has been, a health risk to regular users of the building, and more than 200 air quality readings, taken since September 2016, support this belief.
"But this asbestos cannot be removed while the building is occupied, so we have decided to close the building while expert contractors carry out remedial works.
"We apologise to staff and students for the inconvenience that this unprecedented situation will cause, and we will do all we can to support them so that research and teaching can continue."
Prolonged inhalation of asbestos fibres can cause illnesses including lung cancer, mesothelioma, and asbestosis.

Cagney the Lhasa apso was trapped for about an hour in her Salford home until the chair's metal frame was dismantled.
Her owner Lyn Kirkwood said she had been searching for the pooch until she "heard a whimper" and saw her back legs sticking out of the chair.
Seven-year-old Cagney seemed "unfazed" after her ordeal, RSPCA officer David Hatton added.
Mrs Kirkwood said the experience had been "horrendous" and that she noticed something was wrong when the Cagney did not bark as usual when her husband's carer visited on Thursday.
After she saw the back legs of the clumsy canine sticking out of the chair, she decided to call for help.
"We called the fire service and the RSPCA, and we had three firefighters with tools trying to get her out," she said.
"When they freed her she just walked off as if nothing had happened."
Fire crew manager Dave Minto said Cagney was "quite distressed" when they arrived but when she saw the crew, she calmed down and "just sat there in total silence".
He said they switched off the electricity supply and took the chair's mechanism apart, freeing Cagney.
Despite her ordeal, Cagney was uninjured and has since "made a full recovery", a spokesperson from Greater Manchester Fire and Rescue said.
Mr Hatton added: "She just wandered off for a drink and came and sat by her owner. It was definitely a first for us though."

The 33-1 shot, ridden by David Mullins and trained by Mouse Morris, triumphed at Aintree in April to become the first novice to win the race since 1958.
The nine-year-old, owned by the Gigginstown House Stud, has twice recovered from a cracked pelvis.
"We didn't want to send him back to Aintree with a big weight, that wouldn't be fair," said Gigginstown's racing manager Eddie O'Leary.
"He provided us with our first Grand National and we'll never forget him."
BBC horse racing correspondent Cornelius Lysaght:
"As the first Grand National winner for owner Michael O'Leary's burgeoning Gigginstown House Stud as well as the first novice chaser to win the race in nearly 60 years, Rule The World has his place in history.
"Though he ran highly respectably at Punchestown after Aintree, O'Leary had already hinted that, having defied serious injury to reach one of the great pinnacles, he had perhaps done his bit.
"What a season for Gigginstown, with success at Aintree, in the Irish National and Cheltenham Gold Cup, but at a price. Rule the World has been retired and there are doubts whether Gold Cup winner Don Cossack will race again."
About 1,650 staff and students will have to move out of an Oxford University building for up to two years after asbestos was discovered.
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A dog has been rescued by firefighters after getting wedged in an electric reclining armchair.
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This year's Grand National winner Rule The World has been retired.