Welbeck was absent along with Tom Cleverley, Nemanja Vidic and Rio Ferdinand - all of whom missed Saturday's 1-1 draw with Southampton.
Vidic and Ferdinand's continued absence means manager David Moyes is likely to pair two from Chris Smalling, Jonny Evans and Phil Jones in central defence.
Patrice Evra suffered a slight knock to his left leg but recovered sufficiently to play a full part in the session and should be fit.
Adnan Januzaj took part in the training session after being added to the Champions League squad as a home-grown player.
Another positive for United saw Darren Fletcher taking part with the main squad after several weeks working on his own to regain fitness.
The 29-year-old midfielder has been battling a chronic bowel condition and has made only seven starts in the past two years - his most recent was on Boxing Day last year - but there are hopes that he could return to competitive action later this month.
United should go into Wednesday's match full of confidence as Sociedad have struggled in the Champions League, losing both their opening games, 2-0 at home to Shakhtar Donetsk and 2-1 away at Bayer Leverkusen.
You can watch David Moyes' pre-match press conference on Sky Sports News from around 1.30pm - Manchester United v Real Sociedad is live on Sky 1HD and Sky Sports 2 HD on Wednesday night from 7.30pm.