The former West Indies seamer was injured while playing football during the warm-up in a County Championship match against Yorkshire in April.
Edwards, 34, is on crutches following an operation.
"His injury is pretty bad and I think that it would be best to get him right for next season," Hampshire coach Dale Benkenstein told BBC Radio Solent.
Fellow ex-Windies pace bowler Tino Best has joined the county on a short-term deal in Edwards' absence.
Benkenstein admitted the chance of seeing the Barbados duo, both signed as non-overseas players under the Kolpak ruling, sharing the new ball for Hampshire would have to wait.
"You never know, maybe next year," he added. "Fidel is very fit and some people heal quicker than others.
"But, as a fast bowler and with the force he puts through his body, an injury like that might be asking a bit too much from him."
Hampshire fast bowler Fidel Edwards is set to miss the rest of the season after surgery on a broken ankle.