Nicknamed "El Mono" (monkey) whilst in Argentina, Navarro Montoya was born in Medellín, Colombia, and he started playing professionally in the former country at only 18, with Club Atlético Vélez Sarsfield. In 1988, after one year in his homeland with Independiente Santa Fe, he joined Boca Juniors, where he would rarely miss a game in nearly ten years – never played in fewer than 35 matches in his full seasons – also setting club records of consecutive games (180) and minutes without conceding a goal (824), and eventually appearing in 396 official games for the "Xeneizes". His last appearance, however, ended in defeat, 1–3 at Club Atlético Banfield.