The party will choose candidates for the remaining five Scottish constituencies by the end of the week, following consultation with local members.
Its national executive ruled on Saturday that Natalie McGarry and Michelle Thomson, who were elected as SNP MPs but now sit as independent members, are not eligible for reselection.
The party is also seeking candidates for the three Scottish seats it did not win in 2015.
The SNP’s national executive met in Glasgow on Saturday to decide the selection procedures for the snap ballot in June.
Candidates will be chosen for Dumfriesshire, Clydesdale and Tweeddale, held by Conservative MP and Scottish Secretary David Mundell, the Orkney and Shetland seat of Liberal Democrat Alistair Carmichael, and Labour MP Ian Murray’s Edinburgh South seat.
Ms McGarry’s Glasgow East seat and Ms Thomson’s Edinburgh West seat will also be fought by new SNP candidates.
Ms Thomson has already confirmed she will not contest the election as an independent, and expressed disappointment with the party’s decision.
SNP depute leader and leader of the SNP at Westminster Angus Robertson said: “This general election is fundamental to what sort of country we want to be. We cannot let the Tories inflict deeper cuts and further austerity on Scotland.
“While the Tories are putting cynical party interests first, the SNP will always put Scotland first.
“SNP MPs have been the hardest working group at Westminster and, with Labour in complete disarray, the only real opposition to the Tory government.
“Over the coming weeks we will work harder than ever to retain the trust of people in every community across Scotland.
“Now more than ever Scotland needs strong SNP opposition to an emboldened Tory government who think they can do what they want to Scotland and get away with it.”