Medvedev ordered government officials to act after a top-flight game between Dynamo Moscow and Zenit St Petersburg on Saturday was abandoned after the Dynamo goalkeeper suffered an eye injury from firecrackers thrown by fans.
"It was a deliberate criminal act, therefore we must change the legislation to try to prevent such unlawful acts in the future," Medvedev told senior ministers at a meeting.
"Such crimes cannot go unpunished, you have to go to jail if you commit them."
Police arrested 53 people, including three female Zenit supporters, on Saturday and charged them with throwing the firecracker that injured Anton Shunin.
The 25-year-old Russia international suffered burns to his cornea in both eyes and some loss of hearing in his right ear.
A disciplinary hearing by the Russian FA was scheduled for Thursday.
Zenit and Dynamo blamed each other for the incident.
Violent incidents have been rife in Russian football as the country is getting ready to host the 2018 World Cup.
Both Zenit and Dynamo have a history of fan violence.
Last year, UEFA fined Zenit £44,000 after their fans lit flares and the pitch became enveloped with heavy smoke during a Champions League match at home to Cyprus club APOEL Nicosia.
Last month, a Russian Cup match between Dynamo and Torpedo in Moscow was abandoned for the same reason. Hosts Torpedo were handed a 3-0 defeat and had to play their next three home games at an empty arena.
Also last month, a group of Dynamo fans in camouflage shot at players using paintball rifles at the club's training ground.