The Scotland full-back limped off before half-time and is certainly out of Sunday’s trip to Bramall Lane, with his involvement in this summer’s European Championships also thrown into doubt.
Norwegian forward Martin Ødegaard is being assessed by Arsenal’s medical staff ahead of their Europa League quarter-final first leg against Slavia Prague tomorrow, while the Gunners expect David Luiz to “be back to full fitness and available for selection in the upcoming weeks.”
"We will assess him today how he’s feeling," Arteta said of Ødegaard.
"He’s been carrying an injury for the last few days since he got injured with the national team."
But there was better news for the Arsenal boss with Bukayo Saka, Emile Smith Rowe and Granit Xhaka all available for selection against United.
Arsenal boss Mikel Arteta would not be drawn on when he believes Tierney will return to action.
"We have to make sure first that he doesn't need any surgery, which it doesn't look like," he said.
"The timeframe will be that. It could have been worse because the action looks quite scary, but he looks a bit better and the damage was not that bad, so at the end of the day it is not the bad news we could have been waiting for.
"We are going to have to go day by day and see how Kieran is feeling, then when he gets close to playing time and how he is feeling we will make that decision."
Asked if he thinks Tierney will be fit to play for Scotland at this summer’s Euros, Arteta added: “It will depend how things evolve again in the next few weeks."
Tierney is a Scotland teammate of John Fleck, Oli McBurnie and Oli Burke and plays a key role in Steve Clarke’s system, which helped the Scots qualify for their first major tournament since 1998 when they beat Serbia in their play-off final on penalties.