Jones, 19, was forced off after just 15 minutes at Emirates Stadium after falling awkwardly on his ankle and now looks set to be out until mid-February.
Only Wayne Rooney, Nani and Patrice Evra have played more games this season than the England defender, who has become a regular fixture in Ferguson's starting line-up in his debut campaign, and his absence will be a major blow.
United have been ravaged by injury problems over the past few months with Rio Ferdinand, Anderson, Ashley Young, Tom Cleverley and Michael Owen all currently out, while Nemanja Vidic and Darren Fletcher will not play again this season.
There were further concerns over the fitness of Nani, who left the stadium in a protective boot after being substituted in the second half, as well as Rooney and Michael Carrick,
"It's not good news for us," Ferguson said. "I think Jones will be out for a few weeks - it's ankle ligaments. Carrick was feeling his hamstring in the second half and he just had to sit in the middle of the pitch."