Gov. Tim Walz has tested positive for COVID-19 along with his wife and son, as breakthrough cases have been on the rise.

The governor's announcement Tuesday comes as he has been beseeching Minnesotans to get vaccinated and take precautions around the holidays. He said he does not have symptoms, but he is in quarantine and working from home.

His son, who is in ninth grade, tested positive for COVID-19 on Monday and has sniffles, a sore throat and congestion, Walz said in a video announcement. Walz and his wife, Gwen, first tested negative for the virus Monday morning. They then took another test, which came back positive that night.

"Thankfully, my son has mild symptoms and Gwen and I have no symptoms. My son is vaccinated, and Gwen and I are vaccinated and have received our booster shots, and I am confident that these vaccines are protecting my family and me from serious illness," Walz said in a statement.

The governor's news comes as the fourth wave of the virus to hit Minnesota appears to have peaked in November. The state on Tuesday reported a decline in the positivity rate of COVID-19 testing to 9.1%, below the high-risk threshold of 10%. Hospitalizations for the virus also declined from 1,678 on Dec. 9 to 1,470 Monday, but critical care capacity remained stretched with 97% of adult intensive care beds filled in Minnesota.

State health officials are urging people to be cautious over the holidays and warning that an increase in cases could overwhelm Minnesota hospitals.

People will be gathering with family and friends as the more contagious omicron variant is sweeping the country. Federal health officials said nearly three-quarters of new cases last week involved that variant.

"The omicron variant and others are out there. But the fact of the matter is that we have the vaccines and we have protocols that help make this doable, keep folks out of the hospital. It's disappointing, I was looking forward to Christmas with my relatives … but those things will have to wait," Walz said in his video announcement. "If you are feeling these sniffles, get tested right away. Isolate then. Certainly make sure you are getting your boosters."

The DFL governor received the Johnson & Johnson vaccine at the end of March alongside former Republican Gov. Tim Pawlenty, in an attempt to encourage all Minnesotans to get vaccinated. The pair also got their booster shots together in October, and Walz received a Moderna dose at that time.

Breakthrough infections in fully vaccinated Minnesotans have been an increasing part of the latest pandemic wave. They made up 44% of the 23,584 infections and 168 COVID-19 deaths in the week ending Nov. 13, according to the latest state breakthrough data released Monday.

However, unvaccinated people remain at greatest risk of severe illness, hospitalization and death. Allina Health reported that 66 of its 78 COVID-19 patients receiving intensive care on Monday were unvaccinated, along with 52 of 60 patients on ventilators.

This is the first time Walz has tested positive for COVID, said the governor's spokeswoman, Claire Lancaster, although he has had to quarantine after past exposures.

Walz said his family will continue to isolate and he will work from the governor's residence until he tests negative. The governor had several calls on his public calendar on Tuesday. He was scheduled to participate in a ceremonial bill signing Monday that was canceled.

Under the Minnesota Department of Health's guidance, the governor's office needed to notify the organizers of any event Walz had attended since Friday, Lancaster said. She said the only in-person event Walz participated in was a gathering Saturday for the Hmong 18 Council's new president.

Lt. Gov. Peggy Flanagan, who has been vaccinated, and her daughter also tested positive for COVID-19 in October.

"I encourage every Minnesotan to get tested before the holidays, and to roll up their sleeves and get their vaccine and their booster to ensure they, too, have strong protection against COVID-19," Walz said.

The Walz administration announced a "Celebrate Safely, Minnesota" campaign last week, with community testing sites in the Twin Cities opening earlier, starting Monday, and the Duluth site expanding its testing hours. Free testing is available at 21 different locations across the state.

Staff writer Jeremy Olson contributed to this report.