Crabtree was operated on Wednesday, one day after suffering the injury during an organized team activity.
"Michael Crabtree underwent surgery to repair his Achilles tendon that he tore yesterday," coach Jim Harbaugh said. "Surgery was successful and we do not anticipate it will be season-ending for Michael."
Harbaugh would not speculate when Crabtree might return to play.
"I go hard for my friends, family and fans, just felt like I let everybody down," Crabtree wrote on Twitter. "But I'll be back ready!! I promise!"
While a torn Achilles usually is considered a season-ending injury, Baltimore Ravens linebacker Terrell Suggs and Tampa Bay Buccaneers defensive end Da'Quan Bowers were able to return to play during last season after suffering the injury earlier in the year.
USA Today first reported that Crabtree was hurt during Tuesday's OTA, citing an unidentified source.
Harbaugh said Crabtree went in motion, planted to begin a route and "felt like somebody kicked him in the Achilles, which sometimes people say that feels like." Having the operation right away was considered the best option so Crabtree has the chance to return this year -- unlike with running back Kendall Hunter last season, who had the same injury but the decision was made to wait some time before surgery.
"Good news is he woke up from the surgery and the first thing, asked the doctor how it went," Harbaugh said. "(The doctor) talked about the success of the surgery and he didn't anticipate he'd be out for the year. His comment to that was, 'Got no choice but to be back.' Every day now is a healing day, and that starts today."
The 25-year-old Crabtree, the team's 10th overall pick in the 2009 draft out of Texas Tech, had career highs last season with 85 receptions for 1,105 yards and nine touchdowns for the NFC champion Niners, who lost 34-31 to the Ravens in the Super Bowl.
In the postseason, Crabtree had 28 receptions for 285 yards and three touchdowns, including one score in the 49ers' Super Bowl loss to the Baltimore Ravens.
This could be a major setback for the two-time defending NFC West champions after Crabtree's breakout season. He was one of the big reasons the franchise returned to the Super Bowl for the first time in 18 years, clicking with quarterback Colin Kaepernick after his promotion to starter in November over departed 2005 No. 1 overall draft pick Alex Smith.
"It's a setback, but Michael's young, he's strong. Everything will be a positive approach to healing and we'll anticipate great things," Harbaugh said. "Another thing right now is if you look at the young receivers on our team that will emerge because they have to emerge. I'm excited to watch them compete for that spot."
Kaepernick and Crabtree were eager to get back on the field together after falling just short in New Orleans back in February.
Kaepernick's fourth-down throw into the end zone in the closing moments sailed over Crabtree. Harbaugh and the 49ers argued that Crabtree got held, bumped by cornerback Jimmy Smith with safety Ed Reed trailing the play.
Crabtree also had five TDs and 30 catches on third-down plays last season -- both stats among the top five in the NFL.
Harbaugh wouldn't say whether the 49ers would look outside the organization for a replacement with Crabtree out, or even if the team would consider bringing back Randy Moss.
"We're excited for the young receivers that we have, and feel that somebody's going to emerge there," he said. "Competition will create that, and we'll look forward to watching that."
Crabtree has bounced back the past two seasons from several injuries.
After a 71-day contract stalemate as a rookie, Crabtree was sidelined during the 2010 preseason with a neck injury. A year later, he was out with a broken foot sustained while working out in Alex Smith-organized practices during the NFL lockout.
In 2011, Crabtree led the team in catches (72) and yards receiving (874), but San Francisco came up short of a Super Bowl.
While he had four catches for 25 yards and a 4-yard touchdown reception in a 36-32 victory against Drew Brees and the favored Saints in the NFC divisional playoffs, it was the NFC championship game Crabtree remembers as a most disappointing day.
San Francisco's receivers had just one catch for 3 yards -- yes, it was by him -- and Crabtree was targeted four times in a 20-17 overtime loss to the eventual Super Bowl champion New York Giants.
Crabtree said that performance helped fuel him last year.
ESPN Senior NFL Insider Chris Mortensen, ESPN NFL Insider Adam Schefter and The Associated Press contributed to this report.