Bale, who scored with a seventh-minute header to put Real 1-0 up in the La Liga clash at the Bernabeu, limped out shortly before halftime with his side leading 5-0.
Bale has already been sidelined twice this season with calf problems, missing about two weeks each time.
The 26-year-old Wales forward has been in good form in recent weeks and his goal against Gijon was his 13th in the league this season.
Benzema, who netted a first-half double, hobbled off with about 25 minutes left after hurting his foot in a collision with team mate James Rodriguez.
"What Karim has is a knock," coach Zinedine Zidane told a news conference after his side wrapped up a 5-1 victory, with Cristiano Ronaldo also scoring twice.
"Bale's (injury) is more complicated," added the former France and Real great, who was taking charge of his second game after replacing the sacked Rafa Benitez.
"Let's wait for the scan," he added. "We hope it's nothing serious."
Ronaldo and Benzema are La Liga's leading marksmen this season with 16 goals apiece, one more than Barcelona pair Neymar and Luis Suarez.
(Reporting by Iain Rogers, editing by Martyn Herman and Ken Ferris)
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