The Juventus winger will not travel to Moscow for Wednesday's game which will be decisive for both teams.
Brazil top the group and will qualify with a draw but the five-times world champion could go out if they lose to the Serbs.
"At the end of the game yesterday Douglas Costa complained of a pain in the back of his right thigh," doctor Rodrigo Lasmar told reporters. "Exams showed he has a slight muscle injury, a diagnosis confirmed today by a magnetic resonance scan."
Lasmar said full back Danilo, who missed the Costa Rica match with a thigh problem, will also stay at the team's base in Sochi for more treatment.
(Reporting by Andrew Downie, editing by Ed Osmond)
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