The joint GfK, NOP and Ipsos MORI poll on behalf of the BBC, ITV News, and Sky News would see the SNP claim 58 seats, and leave Labour all but wiped out north of the border.
However the SNP, who won just six seats in the last general election, advised the exit poll result be treated with caution.
Ms Sturgeon tweeted: "I'd treat the exit poll with HUGE caution. I'm hoping for a good night but I think 58 seats is unlikely! "
I'd treat the exit poll with HUGE caution. I'm hoping for a good night but I think 58 seats is unlikely! #GE15— Nicola Sturgeon (@NicolaSturgeon) May 7, 2015
Sturgeon added: "Whatever the results, I'm very proud of our campaign."
Kezia Dugdale, deputy leader of the Scottish Labour Party, said she hoped the poll was "badly, badly wrong" because Scotland could not afford another five years of the Tories.
Reacting to the figures, Ruth Davidson, leader of the Scottish Conservatives, said she would be delighted if her party did increase its share of the seats across the country.
But she insisted exit polls should always come with a "health warning".
"I remember 1992," she told BBC Scotland.
The poll suggested the Conservatives would be the largest party at Westminster, winning 316 seats - 10 short of the number needed for an overall majority.
However Sturgeon, the Scottish First Minister, has spent the election campaign arguing that a large block of SNP MPs could lock the Conservatives out of power at Westminster and help bring an end to austerity.
The Labour Party is expected to suffer heavy losses across the country, and is on course to have 239 seats across the UK, with the Liberal Democrats also seeing their numbers reduced.
SNP activists and supporters reacted with shock and pride on social media as the exit poll was announced.
Personally think just to win it north of the border be an incredible achievement anything over 30 be a seismic shift in Scotland #SNP— martin compston (@martin_compston) May 7, 2015
Scotland is so much more united now. #SNP— Helen Kate Galloway (@Omgitshelen) May 7, 2015
Others blamed the SNP vote for the Conservatives' significant majority:
Well thanks #SNP we have a Conservative government well done in the UK— James Hunt (@jameshunt31) May 7, 2015
GENERAL ELECTION 2015