The talks, co-ordinated by SNP Westminster leader Ian Blackford, will involve the leaders of the Liberal Democrats, Plaid Cymru and the Greens, the party said.
The SNP also said there would also be a chair waiting for Jeremy Corbyn at the round-table meeting if he chooses to attend.
Mr Blackford invited the Labour leader to the summit before new year but said he had indicated in a letter that Labour would not attend.
Mr Blackford added: “Extreme Tory plans to drag Scotland and the UK out of the single market and customs union will take a wrecking ball to our economy - destroying hundreds of thousands of jobs, and damaging people’s incomes, livelihoods, and living standards for decades to come.
“As we move into the critical second phase of the Brexit negotiations, and with just over a year to go before the UK is set to leave the EU, time is running out to save the country from this unprecedented economic catastrophe.
“Our hope for the meeting is to build on the consensus with other opposition parties - it is now more important than ever that we have a united and effective opposition focused on protecting our vital single market membership and holding the UK Government to account.
“Short of remaining in the EU, protecting our single market membership is by far the best compromise, the least damaging option, and the only way to safeguard people’s jobs, incomes and living standards.”
Liberal Democrat leader Sir Vince Cable attacked Labour for not attending the event.
“What is disappointing is that the Labour leadership has declined to take part in this summit, even though nearly nine in 10 of their members want them to argue for staying in the single market.
“It is time the Labour leadership came clean and admitted they are tacitly colluding with the Conservatives on Brexit. They are failing their members and the country.”
Labour has dismissed the meeting as a “political gimmick”.