Two people were reportedly taken to hospital after fans clashed outside Bramall Lane.
Reports on social media said two Norwich City fans were taken to A&E following the full-time whistle after violence spilled onto the street.
It was a frustrating afternoon for the Blades as Norwich secured a rare away win after a 23rd minute goal from Yanic Wildschut.
The game was over shadowed by a bottle thrown at Canaries keeper Angus Gunn and the away side's time-wasting as the clock neared the end of the game.
A picture posted on social media shows emergency services huddled around a pool of blood outside the away end.
Danny Jackson posted: "It all started with Norwich fans giving it Wednesday chants and then next thing Sheffield (United) lot kicked off."
Matthew Garrett tweeted: "Not nice to hear about a small portion of Sheffield United fans attacking away supporters, as well as throwing bottles at players! #ncfc"
Edward Seaman posted: "Saw one - innocent I must add - #NCFC fan get knocked clean out. Yes our performance wasn't pretty but no place for violence in football."
Blades fan Steve Lee tweeted: "United fans here - me and my lad caught up in it. Appalled at what happened but in context 99% of Blades are good people. Reflects society."
A South Yorkshire Police spokesman told edp24.co.uk they had arrested a 22-year-old man from Sheffield on suspicion of assault, and a 39-year-old man from Sheffield on a public order offence.