The Brazil international was forced off in the latter stages of his side's 5-2 success, with head coach Carlo Ancelotti revealing after the match that the forward had picked up an injury problem.
"He has a muscle injury. He had a spectacular run when the third goal was scored. It's a shame, but it is what it is," Ancelotti told reporters.
Real Madrid have now confirmed a muscular problem for the 23-year-old, meaning that he will be absent against Barcelona on Saturday night, while it has been claimed that he could be missing until after the November international break.
"Following the tests carried out today on our player Rodrygo Goes by the Real Madrid Medical Services, he has been diagnosed with a muscle injury in the right femoral biceps. Pending evolution," read a statement from the European champions.
Real Madrid confirm muscle injury for Rodrygo
According to journalist Arancha Rodriguez, Rodrygo is expected to be on the sidelines until after the November international break, with the attacker therefore set to miss his side's next four games.
Los Blancos will tackle Barcelona, Valencia, AC Milan and Osasuna before returning to action on November 24 against Leganes, with that fixture potentially marking Rodrygo's return, providing that he does not have a setback in his recovery.
Rodrygo has once again been a vital player for Ancelotti's side this season, making 13 appearances in all competitions, scoring three goals and registering two assists in the process.
The forward's absence could lead to Real Madrid changing formation this weekend for El Clasico, with Jude Bellingham potentially moving into the number 10 position behind Vinicius Junior and Kylian Mbappe.
Which other players are currently injured for Real Madrid?
Real Madrid suffered a double injury blow against Dortmund, with the club revealing on Wednesday that Thibaut Courtois had also picked up a problem which is likely to keep him on the sidelines for the next couple of weeks.
Dani Carvajal and David Alaba are long-term absentees for Los Blancos due to serious knee injuries, although there is a hope that the latter could be back on the field towards the start of 2025.
Brahim Diaz has been missing for the La Liga and European champions since before the September international break due to a hamstring problem, but there is a chance that the Morocco international could be back in the squad this weekend.
Real Madrid are second in the La Liga table, three points behind the leaders Barcelona.