Harbaugh said Crabtree underwent surgery on his right Achilles tendon Wednesday morning at Stanford Hospital but is not expected to miss the entire 2013 season, the San Francisco Chronicle reported.
Some reports indicated Crabtree would be out around six months, putting his return in late November.
The procedure was performed by Dr. Tim McAdams a day after Crabtree sustained the injury while making a cut during a 7-on-7 practice drill.
"The good news is, (Crabtree) woke up from the surgery and the first thing he asked was about how it went," Harbaugh told the newspaper. "(McAdams) talked about the success of the surgery and that he didn't anticipate that he'd be out for the year, and (Crabtree's) comment to that was that he's got no choice but to be back.
"Every day now is a healing day, and that starts today."
The fifth-year player out of Texas Tech emerged as a top receiver last season, finishing with 85 grabs for 1,105 yards and nine touchdowns.
The former 10th-overall choice in the 2009 draft has hauled down 260 passes for 3,345 yards and 21 touchdowns in 58 career games with the 49ers.
Crabtree's absence means newly acquired Anquan Boldin becomes San Francisco's No. 1 wide receiver.