Nainggolan sustained the injury during the weekend's Milan derby, which Inter won 1-0 thanks to Mauro Icardi's injury-time strike.
The Belgium midfielder underwent tests on Monday after he was forced off in the aftermath of a running battle with AC Milan midfielder Lucas Biglia, and it has been confirmed that he will miss a number of weeks, thus ruling him out of the trip to Camp Nou.
Luciano Spalletti was downbeat during his post-match press conference, immediately suggesting that he could face a lengthy absence.
"Nainggolan has been chopped down," Spalletti said to Sky Sport Italia.
"We have to take him to the hospital and see. He won't be with us for a while."
There was better news on the fitness of Croatian duo Ivan Perisic and Marcelo Brozovic, who have both shaken off knocks and are set to feature on Wednesday.
Barcelona have done likewise, meaning their encounter is a pivotal one.
The Catalan club will also be without a key star, with Lionel Messi ruled out of the encounter.
However, he is set to miss three weeks of action, meaning he will be out of both games against Inter, as well as next weekend's Clasico clash with Real Madrid.