The 19-year-old landed awkwardly after jumping to control the ball, and left the pitch in tears in Valladolid.
Manager Luis de la Fuente said Spain must wait for tests amid concerns it could be an anterior cruciate ligament injury.
“This is the ugly part of football. This is the most bitter victory I have ever experienced in my life,” he said.
“It is a very difficult moment for Gavi, Barcelona, the national team and for me – it seems as if we have lost the game.”
Spain, who had already sealed their place at next summer’s European Championships, beat Georgia 3-1 to finish top of Group A.