The 36-year-old Dane has made only four appearances for the Devils, scoring 29 points at an average of 7.29.
The Plymouth side will operate rider replacement to cover Gjedde’s absence in Friday’s Premier League match against Peterborough and have 28 days to find a full-time replacement.
Team manager Lee Trigger said: “Charlie is a proud man and feels that he is not doing the job for us. He is not fulfilling his aspirations and believes he is letting the team down.”
Plymouth will also be without skipper Kyle Newman against Peterborough and have called up Berwick’s Kevin Doolan as a guest replacement.
Newman has spent some time in hospital because of complications following an injury while riding for his Elite League track Poole a couple of weeks ago.
He says: “When I first injured myself I caused a small internal haemorrhage and from that a sepsis infection developed. Once that gets in your bloodstream it can make you very ill, very quickly and can become serious.
“I’ve now been flushed through with antibiotics and fluids to start clearing this out. After the scans came back with nothing else or new we knew we were already on the road to recovery.”
Newman stressed that he will not rush his return to racing for fear of aggravating the problem.
Peterborough also have an injury problem with heat leader Nickolas Porsing ruled out and have yet to announce whether they will bring in a guest or use the rider replacement facility.
They will be spearheaded by Ulrich Ostergaard, a regular and successful visitor to the St Boniface Arena. He will be supported by fellow Danish riders Nikolaj Jakobsen, Michael Palm Toft and Emil Grondal.
At reserve will be British riders Simon Lambert and Tom Perry.
Plymouth: Rider replacement for Charlie Gjedde, Kevin Doolan, Jack Holder, Todd Kurtz, Sam Simota. Reserves: Stefan Nielsen, Ellis Perks.
Peterborough: Ulrich Ostergaard, Emil Grondal, Nikolaj Jakobsen, Michael Palm Toft, guest or rider replacement for Nickolas Porsing. Reserves: Simon Lambert, Tom Perry.