The 26-year-old had to be substituted in the latter stages of the first half at Bernabeu after a challenge with Real Madrid midfielder Federico Valverde.
According to ESPN, De Jong will not be available for Barcelona until next season, with the Netherlands international set to miss out against Valencia, Girona, Real Sociedad, Almeria, Rayo Vallecano and Sevilla in the closing stages of the 2023-24 La Liga campaign.
However, the report claims that the ex-Ajax youngster should be available to represent his country at this summer's European Championship.
De Jong has already spent time out with two separate ankle problems this season, with the midfielder being restricted to 30 appearances in all competitions this term.
Barcelona's La Liga title hopes are all but over
"Tests carried out on Monday have confirmed that first-team player Frenkie de Jong has a right ankle sprain," read a statement from Barcelona earlier this week. "He is out and his recovery will determine his availability."
Barcelona took the lead in the sixth minute of El Clasico, with Andreas Christensen making the breakthrough, but Vinicius Junior levelled the scores from the penalty spot in the 18th minute.
Fermin Lopez sent the Catalan outfit back ahead in the Spanish capital in the 69th minute, but goals from Lucas Vazquez and Jude Bellingham secured a 3-2 success for Real Madrid.
Barcelona are now 11 points behind the division leaders Real Madrid with just six games left, and their focus will be on securing second spot in the table ahead of Girona.
Xavi insists the future is bright for Barcelona
"We were better than Real Madrid. We deserved the three points," Xavi said after the narrow loss in El Clasico.
"Everyone saw that we were better. Imagine when these 17-18 year olds are 20. In the future there will be success.
"In defence, we have been good and they have generated little danger for us. In the first half, we didn't press like we normally do but in the second half we adjusted it.
"The second half was excellent with high pressure. After the second goal, we needed to be calmer. I'm proud of the team, but it's a heavy loss."
At the end of January, Xavi announced that he would be standing down as head coach this summer, but it now appears likely that he will be extending his stay at Camp Nou beyond the end of the campaign.