In August 2015, it was revealed that Leutwiller holds Canadian citizenship and would be interested in playing for Canada should the Canadian Soccer Association approach him. In October 2016, the CSA confirmed that he would take part in a Canadian camp. He made his debut as a half-time substitute against South Korea on 11 November 2016. Leutwiler was named to Canada's 40-man provisional team for the 2017 CONCACAF Gold Cup in June 2017, as well as the final 23-man squad. He was also named to the 2019 CONCACAF Gold Cup squad on May 30, 2019., On July 1, 2021 Leutwiler was named to the squad for the 2021 CONCACAF Gold Cup, his third participation at the tournament.