The 19-year-old Nash had been selected to play for Team Canada in the tournament, which begins Saturday and runs through May 9 in the Czech Republic.
Nash, a native of Brampton, Ontario, had surgery this week for a severe throat infection.
"I am very disappointed that I will not be able to represent my country at this year's world championships," Nash said. "I won a silver medal at the world juniors in the Czech Republic two years ago and was really looking forward to playing in the tournament. I want to wish my teammates all the best and hopefully they will be able to win the gold medal for Canada."
Nash led his team in goals and points (57) this season. He was selected for the NHL All-Star Game, the first teenager accorded the honor since Quebec's Owen Nolan and Pittsburgh's Jaromir Jagr in 1992.