He was a prolific goal scorer and a participant at the 1982 FIFA World Cup. He was also member of the Peru national football team for the qualification stages of the World Cup in Mexico (1986) and Italy (1990). Navarro played a total of 56 games for Peru between 1980 and 1989, scoring 16 goals. He made his debut on 18 July 1980 in a friendly against Uruguay (0-0) in Montevideo. His last game was on 27 August 1989 against Uruguay at a FIFA World Cup Qualifier.
He is remembered for the leg-breaking incident five minutes into the deciding qualifier game between Argentina and Peru in the 1986 FIFA World Cup in Mexico. The Argentine defender Julián Camino broke Navarro’s leg with a tackle. Camino was not expelled from the game. Argentina with Ricardo Gareca tied the game 2-2 and qualified to the World Cup; Argentina would go on to win the 1986 World Cup.