Penedo began his career with Estudiantes de Panamá F.C. and made his first team debut in 2000. He also played in Panamá for Plaza Amador and Árabe Unido. In his first season with Árabe Unido, Penedo helped the club to the apertura and clausura titles. In summer 2005 he joined Italian club Cagliari but did not make any first team appearances. The following season, he moved to Spain to play for Osasuna B in Segunda División B. After one season in Spain, Penedo returned to Central America, signing in Guatemala for Municipal. During his time with Municipal Penedo claimed four league titles.

Penedo made his debut for Panama in June 2003 as a substitute for Francisco Portillo in a 1-0 win over Cuba. He has, as of 11 July 2015, earned a total of 122 caps including an unofficial match against Mexico in 2007, scoring no goals. He represented his country in 26 FIFA World Cup qualification matches and was a member of the Panamanian 2005 & 2013 CONCACAF Gold Cup team, who finished second in both tournaments. Penedo won the golden glove at the 2005 CONCACAF Gold Cup and the 2013 CONCACAF Gold Cup, which is given to the best goalkeeper of the tournament.

On 5 August 2013, the 2015 CONCACAF Gold Cup Bronze medal winning goalkeeper signed with the LA Galaxy. He made his Galaxy debut on 7 August 2013 in a mid-season friendly against AC Milan in the inaugural International Champions Cup. Penedo and the LA Galaxy terminated his contract and parted ways on 29 July 2015.

Penedo officially married Angie Malca in August 2013 and they married in church in January 2015. They have a son, Jaime Matías.

In 2018 he was named in Panama’s 23-man squad for the 2018 FIFA World Cup in Russia. He started in all three of Panama’s matches. After the World Cup, he announced his resignation from international duty.