The party will challenge the decision of BBC executives to exclude it from the debate, and the BBC Trust's rejection of its appeal. It will demand that Mr Salmond is included in Thursday's debate on the economy, or that a fourth debate involving the First Minister, Gordon Brown, David Cameron and Nick Clegg be held prior to 6 May and broadcast UK-wide.
If the BBC and three main UK parties refuse, the SNP will demand Thursday's debate be scrapped.
Mr Salmond wants to use the platform to argue that a hung parliament would be good for the UK, by claiming that it has worked effectively in Scotland, where the SNP has a minority government.
He hopes that this would give his party some leverage in an election, which it has mainly watched from the sidelines.
SNP deputy leader Nicola Sturgeon said: "The fact that we have been able to raise this money in a day and a half simply underlines the strength of feeling people across Scotland have on this issue."
She added: "Donations have come in from ordinary Scots, who simply share our anger at the way Scotland has been treated."
The SNP election campaign co-ordinator, Stewart Hosie, said: "This is a remarkable achievement in around 31 hours. We have embraced the social media and reached the 50,000 target by securing small donations online from over 1,600 donors."
However, opposition parties poured scorn on the SNP's bid, accusing the First Minister of "posturing" and "desperation".
David Mundell, shadow Scottish secretary, said: "Alex Salmond's attempts to be part of the UK leaders' debates is nothing but posturing.
"He has been offered a space on four Scottish leaders' debates and refused three of them.
"He's also strangely silent about being ignored by Jeremy Paxman. David Cameron, Nick Clegg and Gordon Brown have all done interviews with Mr Paxman, but Alex Salmond hasn't made a fuss about this. Clearly, he is more interested in grandstanding than scrutiny."
Nick Clegg, who has benefited most from inclusion in the debates, arguable at the expense of the SNP which has been overtaken by the Lib Dems in the polls in Scotland, called the legal challenge a "measure of desperation on Alex Salmond's part".
He said: "Alex Salmond wants to put up some electronic barrier between Scotland and the rest of the United Kingdom.
"He should pursue his spat with the broadcasters, but he shouldn't penalise the Scottish people."
A Labour spokesman added:
"He is more interested in trying to win newspaper headlines, because he knows he isn't winning the argument."
However, former BBC correspondent and independent MP Martin Bell backed the SNP. He said:
"The exclusion of the SNP and Plaid Cymru has been profoundly unfair to those parties."