The survey taken at polling stations across the UK suggests the Tories could get 314 MPs when all the results have been counted in Thursday's election.
Labour would get 266, the Lib Dems 14, UKIP none and the SNP 34, the GFK/Ipsos MORI poll for BBC/ITV/Sky suggests.
Early results are suggesting a small swing to Labour but it is too early to say if the exit poll is accurate.
Turnout is so far up by 3 points on the 2015 general election, which means it could be close to 70% by the end of the night, the highest since 1997.
Labour's deputy leader Tom Watson, who held his West Bromwich East seat, said the "hours to come look very uncertain", but added: "Theresa May's authority has been undermined by this election. She is a damaged prime minister and her reputation may never recover."
Labour saw off a Conservative challenge to hold Darlington and took Stockton South back from the Conservatives, denting Theresa May's hopes of a revival in the North East of England and a landslide victory.
Labour gained Rutherglen and Hamilton West from the SNP, with an 8.9% swing, suggesting, said polling expert John Curtice, that the SNP "are going to suffer quite substantial losses". The SNP has also lost Angus, in North East Scotland, to the Conservatives.
Labour also held Wrexham, a top Conservative target in Wales and took the Vale of Clwyd from the Conservatives, it's first gain of the night from Mrs May's party.
Labour also took Battersea, in South London, from the Conservatives, with Treasury Minister Jane Ellison losing her seat.
Labour's Shadow Foreign Secretary Emily Thornberry told BBC News: "It is possible that we will form the next government."
She ruled out a coalition, saying Labour would form a minority government in the event of a hung parliament, asking the smaller parties such as the Lib Dems and the SNP to support its programme in a Queen's Speech.
But veteran Conservative Ken Clarke said he believed his party would have a "small overall majority" when all the votes have been counted, although we might not know the result until much later on Friday.
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To get an overall majority, one party needs to get 326 seats.
The exit poll suggests the Conservatives would be 12 short of an overall majority.
It suggests Labour would gain 34 seats, the Conservatives would lose 17 seats, the Lib Dems would gain six and the SNP lose 22 seats.
The Green Party would be unchanged with one seat and Plaid Cymru would still have three MPs, according to the poll.
In total, 30,450 people were interviewed as they exited 144 polling stations across the UK.
If these numbers are correct, Theresa May played a high risk political game and has lost it  - she didn't have to call this election, and only did so in order to give herself a mandate and breathing space during the bumpy ride of Brexit.
Just a few weeks ago at the start of all of this she seemed unassailable, but a shaky campaign and an insurgent Labour Party may have dashed the Tories' hopes.
This exit poll result is not what either parties were predicting privately - this would be another political surprise - the public again defying the expectations of both the main sides.
The Conservatives do look set to be the largest party, it's not clear on these numbers if they will be able to govern alone - Theresa May's promise throughout was to offer her catchphrase "strong and stable leadership" - instead she may end diminished - but only of course, your votes, and the real results, will determine through the course of the night what really happens next.
Evening Standard editor George Osborne, who was sacked as chancellor last year by Theresa May, said, if borne out by actual results, the "catastrophic" exit poll figures would put Mrs May's future as Conservative leader in doubt.
SNP Deputy Leader Stewart Hosie said it would be an "extraordinary thing" for Theresa May "to call this election for narrow party advantage and then, if these numbers are correct, to blow it incredibly".
He said the SNP would still win the election in Scotland, despite the exit poll forecasting substantial losses.
A Lib Dem source said it was "too early" to comment on the exit poll, but added: "In this election holding our own is a good night."
The party ruled out going into coalition with either the Conservatives or Labour.
Green co-leader Caroline Lucas said she could "hardly dare hope" that the exit poll was right, adding: "To be clear, Greens will never support a Tory government."
UKIP leader Paul Nuttall said: "If the exit poll is true then Theresa May has put Brexit in jeopardy. I said at the start this election was wrong. Hubris."
The Conservatives could still secure an overall majority if, as the exit poll suggests, they perform relatively well in constituencies that Labour are defending where a majority of all voters voted Leave in last year's EU referendum.
They would also need to do better in marginal seats they are defending.
If neither of these patterns materialises, but the exit poll's estimate of the overall levels of support for the parties is correct, then the Conservatives could lose their overall majority.
In addition, there is some evidence from the exit poll that the Conservatives will perform relatively well in Wales.
If the exit poll is correct the SNP could suffer heavier losses than was widely anticipated in advance of polling day.
Indeed this, together with clear evidence of a Conservative revival north of the border, may yet provide the Tories with the extra seats that they might need to secure an overall majority.
A total of 650 Westminster MPs will be elected, with more than 45 million people entitled to vote.
Some votes had been cast before Thursday through postal voting, which accounted for 16% of the total electorate at the 2015 general election, when the overall turnout was 66%.
The Tories will be the largest party but may not have a majority, according to the general election exit poll.