Natalie McGarry said the former tabloid editor should “come to parliament in high heels and shadow a day in the life of an MP with the walking that entails”.
In a series of tweets, she added: “I’m serious. That was an invite. Come to parliament in high heels.”
Morgan attracted criticism yesterday after interviewing Nicola Thorp, who was sent home from her job at an accounting firm for refusing to wear heels, on the ITV show Good Morning Britain.
He said: “Ties with collars can be painful and you have to wear them. Many men are told to wear ties in Parliament. Men have a dress code, women don’t, men don’t make a fuss about it.”
Morgan’s co-host Susanna Reid said: “I’m not sure you can compare the discomfort of wearing a collar and tie with the pain people are expressing about wearing high heels.”
Glasgow East MP McGarry, who sits as an independent after being suspended from the SNP in 2015, later tweeted that Morgan had not responded to her invite.
She was charged with fraud offences in September last year following an investigation by police after a pro-independence group reported a potential financial discrepancy in its accounts.
The MP has denied any wrongdoing.