In a statement, a spokesperson for The Shard said:
The Shard continues to work with the emergency services and we are in constant discussion with the Greenpeace representatives to ensure the safety of the protestors.
In the interests of public and protestor safety, the building’s emergency response team has advised The View to close with immediate effect.
We apologise to guests for the inconvenience caused and The View will be pleased to honour their tickets either later on today or on a different date.
All three restaurants and our offices remain open at this stage.
We take security, health and safety of all our occupiers and visitors to the building extremely seriously.
Victoria Henry, currently one of six Greenpeace activists climbing exterior of The Shard, says the team has nearly reached the top of the building.
Singers Annie Lennox and Radiohead frontman Thom Yorke, as well as actor Ewan McGregor, have all shown their support to six activists who have been climbing the Shard in protest of oil drilling in the Arctic.
Outside The Shard, crowds gathered and commuters stopped to take pictures of the protesters as they progressed several hundred feet up.
The women are climbing in two groups - three in each.
They are currently about halfway up and appear to have stopped for a break.
Channel 4 News reporter Jim Blakey says police at The Shard think it would be "too dangerous" to attempt to seize the demonstrators currently trying the climb the building.
The met police says it has rope teams ready at the shard but suspect it will be too dangerous to go up and seize the greenpeace protesters..
Nottinghamshire woman Ali Garrigan, 27, is one of the activists climbing The Shard today, according to Greenpeace:
Cold and windy 100m up but smiles and snacks all round
In a statement on the Greenpeace website, she said: "We're climbing this building because it's time to draw a line in the ice and say to the oil companies you come no further."
Responding to the demonstration at The Shard in protest at Arctic drilling by oil firm Shell, a company spokesman said:
We respect the right of individuals and organisations to engage in a free and frank exchange of views about our operations.
Recognising the right of individuals to express their point of view, we only ask that they do so with their safety and the safety of others, including Shell personnel and customers, in mind.
The company said oil and gas production from the Arctic was not new.
"The Arctic region currently produces about 10% of the world's oil and 25% of its gas," it said in a statement.
Greenpeace has released video which shows how six activists accessed exterior of The Shard before attempting to reach the top of the 310m-high building.
One of the campaigners said they plan to unveil a "huge artwork" near the summit of the structure.
Greenpeace says Victoria Henry, a Canadian living in London, is one of the climbers scaling The Shard.
This morning she tweeted about the "months of training and secrecy" leading up to the stunt: