The England international, who had been expected to be part of Roy Hodgson's 23-man squad for the World Cup in Brazil this summer, was forced off in the opening exchanges of the Old Trafford clash.
Jones sustained the problem with his left shoulder after a shuddering collision with Maynor Figueroa in the 17th minute as he threw himself at a corner from Adnan Januzaj.
The 22-year-old was clearly unhappy as he left the field grimacing and cursing and he headed straight down the tunnel for treatment in the dressing room, with Nemanja Vidic sent on for his final Old Trafford appearance.
Jones was then taken to a local hospital with his arm in a sling as a precautionary measure, but there will be concerns over his place in Hodgson's squad, which is due to be named on Monday.
The youngster has been a regular in the party for his country and is capable of operating at full-back, centre-back or in the centre of midfield.
Interim boss Ryan Giggs told Sky Sports after the match: "He has gone off to hospital to see what it was. I'm not sure if his shoulder came out or not.
"Hopefully he'll be OK. It's too near to say what the condition is."
Skysports.com readers had expected that Jones would be part of the squad for the tournament in Brazil this summer.
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