Monasterio secured his maiden European Tour title when he charged through the field to win the 2006 Aa St Omer Open. He had won the previous year on the Challenge Tour, capturing the Abierto Telefonica Moviles de Guatemala.
 
Monasterio was crowned Rookie of the Year on the Legends Tour in 2014 following his win at the English Senior Open. He became just the second South American to win the coveted award since it was launched in 1998, after Brazilian Priscillo Diniz in 2000.

His most recent appearances were in 2024, where he participated in several Legends Tour events, including the Sergio Melpignano Senior Italian Open, the Legends Open de France, the European Legends Cup.