Billy McAllister, 48, was fined £200 for shouting and swearing at a man at a meeting on the so-called bedroom tax.
Mr McAllister twice swore at John Park, who has metal plates in his leg and a crushed vertebrae, when they went to a meeting in Possilpark.
On Monday, Mr McAllister pled guilty at Glasgow Sheriff Court to acting in a threatening or abusive manner and shouting, swearing and gesticulating aggressively towards Mr Park.
Shadow Scottish Secretary and Labour Glasgow East MP Margaret Curran has written to Deputy First Minister Nicola Sturgeon calling on the SNP to take action against the councillor.
In her letter Ms Curran said: "I am sure you agree with me that such a verbal assault on a disabled person is completely unacceptable especially from someone holding a senior position within your party. The people of Glasgow will expect you and your party to take action in light of Cllr McAllister's conviction."
Ms Curran has been joined in her calls by Maria Fyfe, former MP for Glasgow Maryhill, which forms part of Mr McAllister's ward.
"Ms Fyfe questioned why "a man like this is elevated to such a senior position in their party in Scotland's largest city".
Matters could come to a head next week at the AGM of the SNP group in Glasgow, where councillors were due to elect a replacement for group leader Graeme Hendry.
An SNP spokesman said: "This is an internal disciplinary matter."