The team said Friday that defensemen Chris Tanev and Nikita Tryamkin, and forwards Mike Chaput and Markus Granlund have shown symptoms. The players with symptoms were immediately tested and quarantined for a five-day period or until test results prove negative.
The team could be without the five players when it hosts the San Jose Sharks on Saturday.
Canucks general manager Jim Benning said the team was hoping the virus did not continue to spread.
"We're sitting here with our fingers crossed," Benning told The Province. "We don't know if there will be more. If anyone else calls in with swollen glands, or they're sick or they're not feeling well, we will get going right away on the process and get their bloodwork done."
Blood tests for several of the players were expected back later Friday, and if the tests come back negative, the players would be available to play Tuesday against the Detroit Red Wings, The Province reported.
Benning said the team would recall defenseman Evan McEneny and forward Alex Grenier for Saturday's game against the Sharks, according to The Province.
Benning told the newspaper that the team first learned of the problem on Wednesday.
"One of our players had woken up Monday and had swollen glands. That was the start of it," he told The Province. "The last two days, the other guys have popped up with swollen glands."
In a statement issued Friday, the Canucks said that vaccines are being administered to minimize further risk of contraction, along with universal preventative hygiene measures, including disinfecting all dressing room areas.
The NHL also sent a memo to all 30 teams, reminding them of the precautions that should be taken for mumps.
The mumps virus is found in saliva and respiratory droplets. It is spread person to person through coughing, sneezing or coming into contact with saliva.
The outbreak with the Canucks came on the same day public health officials and infectious disease experts urged Canadians to check that their vaccinations were up-to-date, as clusters of mumps are being investigated in Ontario and Alberta. Measles cases are also being probed in Nova Scotia. In Alberta, seven players and a coach with the Medicine Hat Tigers of the Western Hockey League have been hit by mumps.
The Associated Press contributed to this report.