The 19-year-old left wing was expected to make his debut for the Canadian national team. He helped Canada win a silver medal at the 2002 world junior championship.
The world championships begin Saturday in the Czech Republic and end May 9.
"I was really looking forward to playing in the tournament," Nash said in a statement released Thursday by the Blue Jackets and Hockey Canada. "I want to wish my teammates all the best and hopefully they will be able to win the gold medal for Canada."