The Tragically Hip, the Canadian rock band, announced Tuesday that its lead singer, Gord Downie, had been given a diagnosis of terminal brain cancer. But doctors have cleared Mr. Downie to go on tour for a series of summer concerts.

“This feels like the right thing to do now, for Gord, and for all of us,” the Hip said in the statement on its website.

Mr. Downie, 52, is a household name in Canada, and the news of his illness quickly lit up social media, to the puzzlement of some beyond the country’s border.

As the frontman and lyricist for the group fondly known as “Canada’s band,” he writes songs that are rooted in his experience of and love for his country.

That has earned the band thousands of fans, including Canada’s prime minister, Justin Trudeau, who pinned a statement honoring Mr. Downie to the top of his Twitter page on Tuesday.