Earlier this week, Mr McAllister was fined £200 at Glasgow Sheriff Court after pleading guilty to acting in a threatening or abusive manner, shouting swearing and gesticulating aggressively at a man who classes himself as disabled.
Margaret Curran, Labour MP for Glasgow East and Shadow Secretary of State for Scotland, has written to the Deputy First Minister demanding that she takes action.
In her letter Ms Curran says: "You will no doubt be aware of the concern among Glaswegians that such a man holds high office in your party and the city of Glasgow.
"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.
"I would therefore call on you as a fellow Glasgow elected member and Deputy Leader of the SNP to take immediate action to ensure this individual is no longer allowed to hold a senior position in the SNP.
"It is clear from this conviction that he is not a fit person to hold office in Glasgow City Council.
"I would be grateful if you could clarify if you think he is fit to hold office within your party.
"The people of Glasgow will expect you and your party to take action in light of councillor McAllister's conviction."
Ms Curran insisted Mr McAllister had brought both the SNP and Glasgow City Council into disrepute.
She added: "The SNP should do the right thing and seek Mr McAllister's resignation as a councillor as well as being their deputy leader on the council."
Former Labour MP for Maryhill Maria Fyfe also called for action by the SNP against the senior councillor.
She said: "What does it say about the SNP when a man like this is elevated to such a senior position in their party in Scotland's largest city?
"The SNP must take swift action against a man who has now been convicted of acting in a threatening or abusive manner."
An spokesman for the SNP said: "This is an internal disciplinary matter."