Workers say there are already shortages in equipment and manpower, meaning New York’s emergency response system could be hamstrung as the virus works its way through the Fire Department and the city.

Staffing numbers for E.M.S. workers are so low, union officials say, that any moderate infection within the ranks could affect dozens of shifts, slowing units’ response time in neighborhoods across the city.

“The city is going have to make decisions on what responses they are going to send ambulances to, and what they are not,” said Bradford Billet, the former associate director of the city’s E.M.S. division. “These are not regular times.”

On Wednesday night, the Fire Department changed its quarantine guidance for emergency workers and firefighters, saying they would be required to work even if they had been exposed to the coronavirus — as long as they were asymptomatic.

The guidance was in line with what the New York State Department of Health had suggested in recent days for health care facilities, the Fire Department said in an announcement to its staff, which was provided to The New York Times. All those currently under quarantine would remain so.