Martinez began his career with top Costa Rican side Deportivo Saprissa. His first appearance with the club was in the 2009 Torneo de Invierno, this coming after a successful role in the 2009 FIFA U-20 World Cup. Martinez won one title with the club during the 2009–10 Costa Rican Primera División season the Campeonato de Verano 2010. Josué was an important part of The Purple Monster, being one of its top goalscorers in that tournament also scoring the 1-0 winning goal against Liga Deportiva Alajuelense in the first of two matches of "El Clásico" de Costa Rica, at Ricardo Saprissa Stadium in San José. He wore the number 28 for Saprissa and scored 19 goals in 66 league matches with the club. Martinez also scored an important goal during the CONCACAF Champions League which sent Saprissa to the 2010-11 knockout stage. On October 19, 2010 in a match that was played in Seattle, Martinez's scored an 89th minute goal beating Seattle Sounders goalkeeper, Kasey Keller which helped Saprissa to a 2-1 victory.
Martinez was a prominent member of Costa Rica's 2009 FIFA U-20 World Cup squad, where Costa Rica placed 4th after losing to Hungary in the 3rd place match. He scored two goals in the competition.
Martinez is considered a promising prospect for Costa Rican football and its National Team, he debuted with the full national team in 2009 prior to his debut with the Saprissa first team. He was a member of Costa Rica's 2011 Copa América side, netting 1 goal in 3 matches during the competition.
Scores and results list. Costa Rica's goal tally first.