The 25-year-old was given the nod on the right-hand side for Los Blancos' trip to San Sebastien, but he was forced off the pitch with just 25 minutes on the clock.
Real subsequently confirmed that Diaz had hurt his hip, although they did not give a timeframe on his recovery in their official medical report, simply stating that his progress would be monitored.
However, The Athletic claims that the former Manchester City product is set for a two-month spell on the sidelines, depriving Carlo Ancelotti of a versatile attacking option at a hectic point of the season.
Diaz is therefore not expected back in action until the middle of November if his recovery goes to plan, although Rodrygo is a like-for-like swap on the right-hand side of the attack.
Which Real Madrid games could Diaz miss?
Should the Morocco international take a full eight weeks to recover from his problem, he will sit out a total of 12 games for Real Madrid before a potential comeback after the November international break.
Diaz's first absent game comes as early as Tuesday, when Real Madrid begin the defence of their Champions League crown against Stuttgart, before home La Liga matches with Espanyol and Alaves.
Ancelotti's men then conclude September with a trip to city rivals Atletico Madrid, a few days before travelling to Lille in the Champions League on October 2, and the visit of Villarreal on October 5 precedes the international break.
Real Madrid face two huge battles at the end of October, as they take on Borussia Dortmund in a repeat of the most recent Champions League final four days before the first Clasico of the season against Barcelona.
Diaz is also considered unlikely to make the cut against former team AC Milan on November 5, although he should have made a full recovery in time for Los Blancos' trip to Anfield to face Liverpool on November 27.
The 25-year-old has amassed 15 goals and 13 assists in 71 games for Real Madrid since leaving Man City midway through the 2018-19 season, scoring one and setting up another in a 3-0 success over Real Valladolid on August 25.
Despite losing Diaz prematurely, Real Madrid eased to a 2-0 victory over Real Sociedad thanks to second-half penalties from Vinicius Junior and Kylian Mbappe, moving onto 11 points for the season but remaining four points behind leaders Barcelona.
Which other Real Madrid players are out injured?
Diaz is now one of four long-term absentees in the Real Madrid treatment room, which also houses David Alaba (ACL), Eduardo Camavinga (knee) and Dani Ceballos (ankle).
Jude Bellingham and Aurelien Tchouameni also missed the win over Real Sociedad, but the pair are now back in training with a view to returning against Stuttgart in midweek.