The SNP's national executive has ruled not to endorse two sitting MPs as candidates in the general election.
Ms Thomson withdrew from the SNP whip last year amid an ongoing police investigation into property deals.
She said she was "very disappointed with the decision".
And the Edinburgh West MP confirmed that "after careful consideration" she had decided not to put herself forward for election.
The SNP confirmed on Saturday that all 54 of its sitting MPs would be endorsed as candidates.
The leader of the party at Westminster, Angus Robertson, said: "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."
In a statement, Ms Thomson said: "Since September 2015 there have been reports concerning a solicitor I used some seven years ago.
"I have always made it clear that I have done nothing wrong and it is a matter of public record that it was the solicitor who was under investigation and not myself, that no charges have ever been brought and that I assisted PS (Police Scotland) on a purely voluntary basis.
"I must note that, even in political parties, the concept of natural justice must apply, as must the need for defined processes that are applied fairly, rigorously and transparently.
"I would advise the SNP to employ the services of an external body to help them develop a process as soon as possible."
She added: "I have been privileged to be the MP for Edinburgh West. After careful consideration I have decided not to stand again at this time and I would encourage all the political parties to avoid personal smears and instead focus on what people really want to hear about."
Ms McGarry failed to receive the party's endorsement as a general election candidate following allegations of fraud.
She tweeted: "Today's decision by the SNP NEC was of no surprise to me. I'll be making no statement. My focus remains with my constituents & staff."
The UK goes to the polls on 8 June after Prime Minister Theresa May announced plans for a snap election, subsequently endorsed by MPs by 552 votes to 13.
The SNP now needs to find five candidates, including three for the seats the party did not win in 2015.
A number of party activists have already announced their intention to bid for the SNP ticket in the Glasgow East and Edinburgh West seats formerly occupied by Ms McGarry and Ms Thomson.
The other three constituencies where candidates have still to be selected are Dumfriesshire, Clydesdale and Tweeddale, Edinburgh South, and Orkney and Shetland.