The management team at the Devonshire Cat, on Wellington Street in the city centre, said they were forced to close this afternoon following the incident.
They said staff safety was a top priority for them.
Posting on Facebook, they said: "This is a completely new experience to us, as we are very fortunate to enjoy a good relationship with both our wonderful Blades fans and away fans.
"We also know this is only a small section and not a reflection of the club in question. We prioritise staff safety over everything else and as such at this time we're unsure when we'll be reopening but we'll be sure to let you know as soon as we've made a decision.
"We appreciate your understanding in this matter and apologise for any inconvenience caused."
In a later update, the team thanked everyone for their patience and concern adding the pub would reopen at 7pm.
The kitchen is to remain closed until tomorrow.
Sheffield United took on Leicester City today, losing in a 2-1 defeat to the side at home at Bramall Lane.