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Wilson's wife, CTV Ottawa's Patricia Boal, revealed the diagnosis on a newscast Friday night, according to Garrioch.
Local health officials informed him Friday that he is infected. Wilson was tested for the virus last week.
The 59-year-old felt ill for several days after returning from the Senators' California road trip on March 12, the same day the NHL paused its season amid the pandemic. On Boal's advice, he got tested, and has been self-isolating since returning home.
"It's hit me hard enough," Wilson said. "I haven't felt good for two weeks. The worst was last weekend. So I'm hitting a week here at least with shortness of breath and feeling lethargic. I walk up a flight of steps here and I’m out of breath.
"The biggest thing is the lack of taste and smell. I'm down about eight or nine pounds. I’m not eating as much."
Wilson provided a further update later in the evening.
Former Senators superstar and current San Jose Sharks defenseman Erik Karlsson was among many who tweeted well wishes to Wilson.
Wilson, who provides radio commentary for Senators games, is the third member of the team's traveling group to test positive for COVID-19. Two unnamed Senators players have contracted the virus, as have two from the Colorado Avalanche.
Earlier Friday, the St. Louis Blues announced broadcaster John Kelly had been diagnosed with the coronavirus but is now symptom-free.