Crabtree, San Francisco's leading receiver last season when they reached the Super Bowl before being beaten 34-31 by the Baltimore Ravens, injured his right Achilles during an organized team activity on Tuesday.
"(Coach) Jim Harbaugh tells media @KingCrab15 has torn Achilles tendon but has had successful surgery. Crabtree not expected to miss full season," the 49ers tweeted on Wednesday.
"We feel like someone is going to emerge there," Harbaugh later told reporters about the challenge facing the 49ers' younger receivers in Crabtree's absence.
Crabtree, 25, caught 20 passes for 285 yards and three touchdowns in last season's playoffs after setting career-best marks with 1,105 yards, nine touchdowns and 85 receptions during the regular season.