Grieg Seafoods, which operates the facility in Loch Snizort, a sea loch to the north-west of the island, said damage to one its pens was discovered by a diver during a routine check on February.
The Norwegian-based company estimates 21,700 fish, with an average weight of 2kg, managed to escape.
Grant Cumming, managing director Grieg Seafood Shetland Ltd, said: “Our priority is to prevent escape and a temporary mend to secure net was immediately applied.
“Marine Scotland were informed of the incident and the net was repaired the same day. Since then we have counted the fish in the net and regrettably estimate that we have lost 21,700 fish. The fish were in good health and had not received any medicines lately.
“We are conducting an in-depth investigation to discover the root cause of the breach in the net to ensure it does not reoccur.”