Perez was pulled from his media duties for the race on Thursday at the Buddh International Circuit, with Sauber claiming the Mexican was suffering with a cold.
Sauber have on Friday released a statement which reads: "Due to the fact Sergio is unwell, the team has decided to let its reserve driver Esteban Gutierrez jump into the car for the first free practice session ahead of the Indian Grand Prix on Friday.
"This should help Sergio's speedy recovery so he is able to drive for the remainder of the weekend."
However, via his Twitter account, Perez claimed he was fine to drive.
Translated from Spanish, his tweet reads: "Had a fever yesterday, but I'm all right today [Friday]. It's a team decision."
Perez is due to quit Sauber at the end of the season, replacing Lewis Hamilton at McLaren when the Briton heads to Mercedes.
For Gutierrez, his drive in FP1 was his first taste of a Formula One car over the course of a grand prix weekend. Perez did make a return for the second practice on Friday.