Public Safety Department chiefs did not ensure properly working alternatives were in place before deciding to close the centres.
Pedro Janer, public safety secretary said Puerto Ricans should call the island's emergency management agency at 787-724-0124 or police at 787-343-2020 in an emergency.
Mr Janer said both agencies operate 24 hours a day. But people calling the first number provided could not get through to call handlers, Associated Press (AP) reported.
The callers instead reached a recording system asking them to dial 911 in the event of an emergency. The recording provided callers with a directory.
"This is serious," Nazario Lugo, president of Puerto Rico's Association of Emergency Managers, told AP. He said he was shocked at the government's temporary plan to handle emergencies in the US territory of 3.2 million people.
Mr Lugo said officials should relay 911 calls through to another number, rather than forcing people to call a long number that they would have to read or hear about on the news.
"Response times will definitely be affected," he added.
Kiara Hernandez, a spokeswoman for the Public Safety Department, said she could not immediately comment on why officials were unable to automatically route emergency calls to another number.
"It's an option that's being evaluated," she said.
She also said she didn't know why officials decided to close both 911 centers before ensuring that such alternatives were in place.
It is the first time Puerto Rico has shut down its primary and secondary 911 call centres. Mr Janer said the buildings will be thoroughly cleaned and that he will soon announce when operations at the 911 call centres will resume.
It was unclear how many employees tested positive. Puerto Rico has reported more than 29,700 confirmed cases of coronavirus infections and recorded 770 deaths.
Last week, Puerto Rico's governor announced that more people will be able to visit restaurants, gyms, theatres and casinos as the island relaxed some pandemic-related restrictions.
In addition, public transportation including buses and trains will resume service next week, and ferries will be allowed to only take tourists to the popular nearby island of Culebra.
A 10pm to 5am curfew remains in place, and face masks continue to be mandatory.
“We cannot lower our guard,” said governor Wanda Vázquez.
With Associated Press