Councillor Neale Gibson, Walkley ward, stirred debate on the social media platform when he tweeted saying a 15-year-old girl was responsible for her own death.
He said: 'I think the Pret a Manager case shows that if you have an allergy it's your responsibility to to ask the retailer if the item you are purchasing contains the ingredients you are allergic to.
'It shouldn't be the responsibility of the retailer to list every single ingredient.'
The case he referred to was the death of Natasha Ednan-Laperouse who died in 2016 after she had an allergic reaction to eating a baguette on a British Airways flight from London to Nice.
It did not have any allergen advice on its wrapper as there was no requirement for it to do so because of reduced labelling requirements.
Following the girl's inquest last week the company have committed to fully labelling ingredients.
As a result of his behaviour, the Labour group said they will take disciplinary action.
Coun Peter Rippon, Labour group whip, said: 'These comments are clearly unacceptable and extremely insensitive, they do not reflect the views of Sheffield Labour councillors.
'We will be treating this matter very seriously and will be considering the appropriate disciplinary action to take against the member.'
Coun Gibson's comments also sparked back-lash on Twitter.
Toby Foster, BBC Radio Sheffield presenter, said: 'I have read it and re read it. A Sheffield City Councillor has tweeted that a child the same age as my eldest daughter should take some responsibility for her own death. She shouldn't have eaten sesame. It's insane.'
Coun Gibson replied: 'I'm not saying it's her fault. I'm saying that if you have a life threatening allergy it's your responsibility to ensure that whatever you eat doesn't contain something that's going to kill you. I think people are far too trusting of food labels.'
Liberal Democrats Councillor Shaffaq Mohammed referred to a previous comment made by Coun Gibson when he called some of his constituents 'idiots'.
Coun Mohammed said: 'Not the first time that Coun Gibson has made insensitive comments online, time the Leader of Sheffield Council Coun Julie Dore takes urgent action to discipline him. These comments are totally outrageous and not fitting of a elected representative.'
Ben Graves, Unite Organiser from Barnsley, said: 'How can you check if the ingredients aren't listed in full? You can't exactly lick it and hope for the best. Absolutely ignorant comments to make without even factoring in that this was a child.'
Coun Gibson later deleted the tweets and made his account private and unable to be seen by people who do not already follow him.
Mr Mitchinson said: 'No councillor '“ nor any other elected-to-power individual '“ should be able to lock their electronic door to their electorate. Stand down or stand up to be counted.'
Only a few people defended Coun Gibson's comments.
Craige Timmins, an engineer from Leeds, tweeted: 'It's insensitive in timing, but he has a point of sorts. There's hundreds of allergies, if you have one, you should be asking if your food contains what your allergic to. Had she done so, she'd have been given a folder which listed the ingredients.'
At a full council meeting the next day Julie Dore reminded councillors that 'tweets on sensitive subjects do reflect heavily on the chamber as a whole.'
Coun Gibson declined to comment further.