Edinburgh West MP Christine Jardine said Scotland would already be outside the European Union by the time of any second independence referendum and would have to meet strict EU criteria to get back in.
And she suggested Scotland would struggle to fulfil all the criteria on its own.
Ms Jardine, who hopes to make her Commons debut in the new role at Scottish Questions today, said: “There is no serious suggestion Scotland could be part of the EU immediately after Brexit.
“If people genuinely believe in an independent Scotland I respect that, but if they believe in an independent Scotland as a solution to Brexit, it’s not.”
Ms Jardine insisted Scotland would be best-served remaining in the UK even after Brexit.
She said: “Why would you respond to leaving one single market by leaving the single market you have left?
“We want Scotland to have the best possible relationship with the EU, but as part of the UK.
“The argument the Tories make for leaving the EU is the same argument the SNP makes for leaving the UK.
“The argument we make for staying in the UK is the same argument the SNP make for staying in the EU.”