The suspect is identified as 31-year-old Mark Lugo.
According to witnesses, a man took the artwork from the Weinstein Gallery on Tuesday morning and fled in a waiting taxi.
The gallery says the piece was a 1965 pencil-on-paper drawing titled "Tete de Femme," recently purchased at an auction for $122,500.
Surveillance video from a restaurant several doors down from the gallery showed a man walking by carrying a piece of framed artwork under his arm. He was dressed similarly to the police description of the suspect.
Investigators were able to interview witnesses and subsequently located cab driver and impounded taxi cab for evidence.
More leads led police to a hotel in Napa, where they found and arrested Lugo. He was taken into custody without incident.
The Picasso sketch was also recovered.