The Met Office said the weather warning for the city is valid until Wednesday (February 10) while some other parts in the UK will face significant snow accumulations with amber warnings in place.
This happens when cold air emanating from Russia and Eastern Europe will move across the UK over the coming days, bringing significant snow accumulations to parts of Eastern England and Scotland.
Rain will then increasingly turn to snow on Sunday as the cold air spills across the whole of the UK.
The forecasters said the yellow warnings for snow and ice have also been issued covering the eastern half of the UK from Saturday through to Wednesday.
Met Office Chief Meteorologist, Paul Gundersen, said: “The UK is in for a notably cold and snowy period over the next week, with very cold air in place over the whole of the UK by Sunday.
“Showers will see snow accumulating across eastern areas.”
Sheffield will have a cold start to Sunday with a brisk northeasterly wind, which will continue to bring frequent sleet and snow showers off the North Sea, with a maximum temperature of 2°C.
Snow showers are expected to continue until Wednesday, leading to further snow accumulations and icy stretches.
Despite sunshine in between the showers, it will remain bitterly cold, with often strong winds and severe overnight frosts.
The Met Office also warned that there will be strong easterly winds during this period which may lead to blizzard conditions and blowing and drifting of lying snow at times.
Meanwhile, daytime temperatures will stay in low single figures for much of the country over coming days, with some places staying below freezing and the bitter winds will make it feel even colder.
Here is an hour-by-hour forecast for Sheffield on Sunday.
7am – Overcast
8am – Overcast
9am – Overcast
10am – Cloudy
11am – Light snow
12pm – Light snow
1pm – Light snow
2pm – Overcast
3pm – Light snow shower
4pm – Light snow
5pm – Light snow shower
6pm – Cloudy
7pm – Cloudy
8pm – Cloydy
9pm – Cloudy
10pm – Cloudy
11pm – Cloudy