The Zimbabwe international limped off during the Pilgrims' 2-0 defeat at Hartlepool and went under the knife on Wednesday.
Bhasera is the third Plymouth player to suffer the same injury, with Simon Walton and Damien Johnson also being sidelined.
Manager Peter Reid told the club's official website: "He's had an operation, he's quite happy with it, but it will be a nine-month job.
"It's just one of those things. They are bad injuries, but the way medical science is these days, they usually come back stronger. The most important thing is getting him back."
Source: PA
Source: PA