Vardy came on as a late substitute in normal time of Tuesday's game in Moscow, which ended 1-1 after Yerry Mina cancelled out Harry Kane's penalty with an injury-time equaliser.
The Leicester City striker suffered a groin strain in extra time, during which neither team was able to find a winner.
Vardy had been reportedly set to take England's fifth penalty in the subsequent shoot-out, but Eric Dier stepped up in his stead and scored the decisive spot-kick.
The 31-year-old has started in just one of his three appearances at the tournament, playing the full 90 minutes in the loss to Belgium.
England are set to face Sweden in the last eight in Samara, though Vardy's availability is in doubt as they bid to progress to the semi-finals for the first time since 1990.