The 49-year old Slovenian, who was elected chief of European soccer's governing body in September, said offenders must be banned from entering grounds.
"If they are not stopped, a disaster could happen and Serbia would be in serious danger of getting expelled from a competition. That would be a disaster for Serbia," Ceferin told a news conference at the Serbian FA's headquarters.
He said strong measures must be taken.
"Education is helpful but repression is required too," he said. "UEFA has made it clear to governments in countries where this problem persists that Football Associations alone cannot solve it.
"The state authorities must act in collusion with football bodies to vanquish hooliganism."
Serbia's 2018 World Cup qualifying campaign has so far been incident-free but like neighbouring Croatia, the country has been plagued with violence and incidents of racism since the former Yugoslavia's bloody break-up in the 1990s.
Several nations from the region could qualify for the 2018 tournament in Russia, with Serbia and Croatia topping their qualifying groups while Bosnia and Slovenia have a realistic chance of reaching the playoffs at least.
Describing the 2026 event, the first to feature 48 teams, as a potentially exciting tournament, Ceferin backed the expansion from the present 32-team format as a necessity to involve more fringe nations.
He was also upbeat about the allocation of slots, envisaging 16 teams from Europe, an increase of three from the present 13 although it represents a percentage decline.
"All confederations supported the motion to expand the World Cup to 48 teams and that being the case, it was in UEFA’s best interest to go along rather than to create dissent," Ceferin said.
"UEFA will still be represented by easily the largest number of nations and is the only confederation that will have a team in each group at the 2026 World Cup finals.
Read the full article on eurosport.co.uk: Serbia risking expulsion from big tournaments, says UEFA chief