Beck, a three-time All-Star, is probably best known for his 1993 season. With his wild hair and Fu Manchu mustache, the pitcher nicknamed "Shooter" saved 48 games, a franchise mark that still stands.
Little is known about the circumstances of his death. The Arizona Republic reported that Phoenix police were investigating because Beck was alone at the time of death, but no foul play was suspected.
News of Beck's death reached the Giants clubhouse Sunday a few hours before their game against the New York Yankees, stunning former teammates.
Rich Aurilia, who arrived with the Giants in 1995, laughed as he recalled how much Beck's fearsome appearance on the mound contrasted with the pitcher's gregarious personality.
"I just thought he was a big mean, ol' closer, but he was totally different than that," Aurilia said. "I remember when I met him he came over to say hello with that big high-pitched voice of his. He was a great teammate and a great competitor."
Beck spent 13 seasons in the majors after breaking in with the Giants in 1991. He also pitched for the Chicago Cubs - setting a team record with 51 saves in 1998 - as well as the Boston Red Sox and San Diego Padres.
He finished his career with 286 saves, which ranks 21st all-time. Beck was popular with fans
"It's such a tragedy for him to go at such an early age," said Giants Manager Bruce Bochy, who managed Beck in San Diego. "It's a bad day for baseball. Everybody who played with Rod Beck could tell you what a big heart he had."
Beck ranks second on the Giants' all-time saves list with 199, seven behind Robb Nen. Only four San Francisco pitchers appeared in more games.
Beck was almost equally renowned in San Francisco for his off-the field contributions. He was a key figure in the foundation of the Giants' Until There's a Cure Day, which raised money and awareness for finding a cure for AIDS.
Beck and his wife, Stacey, founded a Pediatric AIDS camp for children inflicted with the disease.
"Everyone in the Giants organization is deeply saddened by the loss of a dear friend," owner Peter Magowan said in a statement. "Rod Beck was a true Giant in every sense of the word - from his dedication on the field to his selflessness away from the park.
"Today, our hearts go out to the Beck family. Rod will be deeply missed."