The first person to test positive for coronavirus in New York City is a health-care worker who acted in a “textbook way” to try to avoid contaminating others after arriving from Iran with her husband, Gov. Andrew Cuomo said Monday.

The 39-year-old woman knew she posed a potential risk after returning — and avoided taking public transportation as she headed home to Manhattan, where she self-isolated, Cuomo said at a press conference with Mayor de Blasio.

The woman took a car service when she and her husband, also a health-care worker, arrived Tuesday, he said.

“We don’t believe she was contagious on the plane or in the private car that took them from the airport to her residence,” he said.

Her husband also is under self-quarantine and is being tested for the illness, “but we’re assuming that he’s positive, given the circumstances,” so he’s undergoing the same protocol as his wife, the governor said, adding that the testing was done at Mount Sinai Hospital, he added.

“The health-care worker has manifested some respiratory illnesses but her condition is mild, so she’s at home,” he said.

Authorities are contacting the rest of the passengers on the couple’s flight, as well as their driver, to try and trace anyone who may have come into contact with her on the plane or in the airport, Cuomo said.

“She was not on any public transportation, she has been in her home virtually isolated and she is isolated once again,” Cuomo told CNN earlier. “So in this case, because of those circumstances — because of her knowledge — she acted in a textbook way.”

Officials also are launching new cleaning protocols at schools, public transportation and other public areas, he added.

“So if people smell — if it smells like bleach when you get on a bus or when a child goes to school, it’s not bad cologne or perfume, it is bleach,” he said.

“In general, there is no doubt that there will be more cases where we find people who test positive. We said early on it wasn’t a question of if but when. This is New York, we’re a gateway to the world. … The whole challenge is about containment of the number of people who become exposed and who become infected,” Cuomo said.

“You’re not going to eliminate the spread but you can limit the spread. Testing is very important and that’s why the CDC, the federal government’s now allowing us to test is a very big deal,” he continued. “We want to get the testing capacity as high as possible. I would like to have a goal of 1,000 tests-per- day capacity.”

The Empire State has received the go-ahead from the feds to perform its own coronavirus testing, noted Cuomo, adding that emergency legislation is in the works to authorize $40 million for extra staff and equipment.

“We should relax because that’s what is dictated by the situation. I understand the anxiety, but the facts back it here,” he said, adding that “we think we have the best health-care system on the planet.”

The governor also said his daughter called him Sunday night and he detected her anxiety.

“She has seen on the news that a person had tested positive and my daughter said, ‘What’s this?’ and I could hear in her voice that she was nervous, and my daughter said, ‘Don’t tell me to relax, tell me why I should be relaxed,’ which is a very big difference there,” he said.

“I want to ensure I tell the people of New York what I tell my daughter: In this situation, the facts defeat fear because the reality is reassuring. It is deep-breath time. First of all, this is not our first rodeo with this type of situation in New York. … When you look at the reality here, about 80 percent of the people with the coronavirus self-resolve.”

In his remarks, de Blasio said that “so far it does not seem to be a disease that focuses on our kids, in fact the opposite. … In fact, the facts are reassuring.

“All New Yorkers should be paying attention to this. We have a lot of information now. The information is giving us things that should give us more reason to stay calm and go about our lives.”

City Health Commissioner Dr. Oxiris Barbot said that “because of the fact that this New Yorker took early action, and there’s no easy indication that it’s easy to transmit by casual contact, there’s no need to do any special anything in the community.

“We want New Yorkers to go about their daily lives. Ride the subway, take the bus, go see your neighbors,” she said.

Hizzoner said he differed with the governor in one respect.

“We don’t think we have the best health-care system, we know we do,” he said, chuckling.