Falcao was brought on in the 65th minute but sustained a hip problem late on in the match which could make him a doubt for Wednesday’s Champions League last 16 second leg against Manchester City.
Monaco scored twice after Falcao entered the pitch with Kylian Mbappe and Joao Moutinho both finding the net to send Leonardo Jardim’s side five points clear at the top of Ligue 1.
Monaco boss Jardim revealed Falcao was sent for tests after the match.
Jardim told a press conference: “He took a major blow on his right side and we will have to see how it evolves. I hope it doesn’t matter and that it is only a small hit, but will wait to see the exams (test results).”
Jardim revealed that Falcao had missed his side’s previous two games against Marseille and Nantes as a precautionary measure.
He added: “Falcao is an important player. He was hampered for 11 or 12 days by a small muscle problem, so we did not take the risk of starting him against Bordeaux.
“He is feeling good and I just hope this injury to his hip is not serious. Because if it is okay, he will start the match against City.”
The 31-year-old forward has been back in form this season after two ill-fated years in England with Manchester United and Chelsea.
He scored a combined total of just five goals for United and Chelsea but has already scored 24 times in all competitions for Monaco this term.