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."

People living in and around Aviemore in the Cairngorms say the water tastes bad and some have blamed it for aggravating skin conditions such as eczema.
Councillor Bill Lobban wants an investigation to check for a link between the water and skin complaints.
Scottish Water said it would look at enhancements to the treatment process.
There have been complaints about the water's taste since the supply came on stream four years ago.
A public meeting in Kincraig, near Aviemore, on Tuesday, which representatives from Scottish Water attended, heard from consumers who believe the water has aggravated skin conditions.
After the meeting, Highland councillor Mr Lobban said skin complaints did appear to be on the rise in the area.
He told BBC Radio Scotland: "I am not a doctor or a scientist so I cannot tell if it is directly attributable to the water or not, but it is something that requires serious investigating.
"It should not be a question of Scottish Water saying basically 'this is a medical problem, go to your doctor'.
"This should be more about Scottish Water liaising with NHS Highland to find out if there potentially is a problem or not."
Scottish Water said it already worked closely with health authorities, including NHS Highland.
A spokesman said: "If a health authority has any concerns over the safety of a water supply, it can impose restrictions on water use, until such times as the matter is investigated and dealt with.
"No restrictions have been imposed in this area and we can reassure customers the water is absolutely safe to use."
The spokesman said the company recognised that "a small number of customers in the Aviemore area" have found the water is not to their taste.
He said: "We want everyone to enjoy the look and taste of their water and continue to liaise closely with the local community, as we work to resolve their concerns.
"That's why we are proposing further enhancements to the treatment processes we use, and are proposing switching to a process called chloramination.
"This is a very well established process and one in four Scottish Water customers currently receive chloraminated water - including those in Inverness, Aberdeen, much of Edinburgh and some other parts of the Highlands and Islands."

The 27-year-old left the Blues for French Top 14 side Toulon in 2014 but his contract expires in the summer.
The Wales international full-back was sat in the stands at the Cardiff Arms Park as the Blues beat the Dragons 27-16 in the Welsh derby on Boxing Day.
"It was great to see him and I know he was quickly back on the plane to his duties in France," Wilson said.
Blues chief executive Richard Holland said earlier in December that they offered Halfpenny a deal to bring him back to Wales.
Speaking after Toulon beat Scarlets in France in the European Champions Cup earlier in December, Halfpenny said he was "weighing up" his options.
"Leigh's obviously got a lot of colleagues and friends from his time with the Blues at the Arms Park," Wilson continued.
"Being home for Christmas I'd imagine with the derby being on his doorstep it was a natural game for him to go and watch."
Halfpenny, who has won 66 caps for Wales, played for Blues for six years before his move to France two years ago.
"I saw him briefly after the game and had a catch up. It's been well documented and I think everybody would like to see Leigh back in Wales," said Wilson.
"Those things are very much ongoing."
Hampshire fast bowler Fidel Edwards is set to miss the rest of the season after surgery on a broken ankle.
[NEXT_CONCEPT]
Scottish Water has said a water supply which has prompted complaints about its quality is safe and "complies 100%" with standards.
[NEXT_CONCEPT]
Cardiff Blues head coach Danny Wilson says it would be good to see Leigh Halfpenny return to Wales