Nationalists previously refused to clap David Cameron after he made his final Commons speech as PM following the Brexit referendum in 2016.
The Conservatives will reveal their new leader on Tuesday morning, with Mrs May expected to formally stand down that same day.
Kirsty Blackman, the SNP’s depute leader at Westminster, told a Sunday newspaper that the party wished the outgoing Tory leader well for the future, but added that its MPs would not “join a cosy Westminster establishment back-slapping exercise” given the Tory leader’s “shameful legacy” in government.
Blackman added that Mrs May “once claimed she would tackle burning injustices – in reality, she has only created them”.
“Theresa May’s shameful legacy in government has left millions of people poorer and worse off,” she told The National.
“Mrs May is leaving the UK in a Brexit crisis of her own making. Throughout her time in office she pandered to the extreme wings of the Tories and the DUP, while ignoring Scotland and refusing to build any consensus across the parliaments and nations of the UK.”
Scottish Conservative MP John Lamont said: “This is another example of the childish behaviour we’ve come to expect from the SNP.
“Regardless of your political views, you should be able to set them aside and acknowledge the service given by an outgoing Prime Minister.
“Instead the SNP are taking part in petty stunts such as this.”