Internationally, Price has represented Canada at various tournaments at junior levels, winning silver medals at the World U-17 Hockey Challenge in 2004 and the IIHF World U18 Championship in 2005. He won a gold medal at the 2007 World Junior Ice Hockey Championships in Sweden. In 2014, Price was named to the Canadian Olympic Hockey Team and won a gold medal at the Winter Olympics in Sochi. Price's play also earned him the tournament's top goaltending award, from the International Ice Hockey Federation (IIHF) directorate. In 2016, Price went undefeated to win his first World Cup of Hockey championship.