The men, in their 20s, were injured in an attack at Crystal on Carver Street at around 2.20am.
They were all taken to hospital, with two of the men having suffered life threatening injuries.
They remain in hospital this morning, where their conditions are described as critical but stable.
The other three were treated for superficial wounds.
South Yorkshire Police said the bar closed after the incident and a search of the venue is underway today.
Enquiries are also being carried out in and around the bar.
On December 23, five men, aged between 21 and 42, were found injured on the Wicker, with four of them having been stabbed.
South Yorkshire Police is investigating whether those stabbings were connected to an earlier incident at Niche nightclub on Walker Street that night.
And in October, two men, aged 28 and 33, were knifed in Area nightclub in Burgess Street, near Barker's Pool.
One was stabbed in the back of his head and the other suffered a punctured lung.
That attack came less than 24 hours after four other men were stabbed in two incidents elsewhere in the city centre.
A 21-year-old man was stabbed in his stomach in Carver Street and three men, aged 20, 22 and 30, were knifed in another attack in nearby Division Street.
Speaking after the violence at Crystal today, Sheffield's District Commander, Chief Superintendent Shaun Morley, said: "This kind of incident cannot be tolerated and we will take positive action in terms of the offenders and licensed premises involved in events like this.
"Pubs and clubs are going to have to improve the way they search those going into their premises. Searching regimes and processes have to be looked at if we are going to negate this issue happening again."