Monaco took advantage of Garcia-Lopez's service problems in a match which had nine breaks of serve.
Monaco, who was a top-10 player in 2012, has won seven of his eight career titles on outdoor clay courts.
He plays Thomaz Bellucci of Brazil, a two-time Gstaad champion, in the quarterfinals.
Bellucci won 6-4, 6-4 against fellow left-hander Federico Delbonis, the fifth-seeded Argentine.
Second-seeded Marcel Granollers of Spain reached the quarterfinals with a 6-1, 6-4 victory over Switzerland's Yann Marti.
Granollers next faces fellow countryman Pablo Andujar, who beat Blaz Rola of Slovenia 6-3, 6-3.
Completing the first-round matches, wild card Henri Laaksonen of Switzerland beat qualifier Gianni Mina of France, 7-6 (5), 7-6 (3).