The young salmon escaped from a farm at Strone Point at Loch Striven in Argyll, operated by Lighthouse Caledonia.
Experts have warned that escapes of farmed salmon carry a threat of spreading disease and of diluting the genetics of wild fish.
The number – 58,800 – is more than the total amount of fish that escaped from Scottish farms last year.
The incident on 16 September was caused by a hole in a net found during a routine inspection.
OddGeir Oddsen, CEO of Lighthouse Caledonia, said: "The loss is regrettable particularly given the progress that has been made over recent months to contain, protect and develop our salmon farms.
"We operate strict regulatory procedures at Lighthouse Caledonia to do all we can to stop such incidents occurring. While we continue to invest in new equipment, all existing nets are checked and serviced on a regular fortnightly basis.
"An investigation has been launched to ascertain how this escape happened. We informed all the relevant authorities and are liaising with wild fish representatives on a recapture strategy.
"As the fish are very small and young, it is unlikely they would survive in the wild."
He said the firm is part of the Containment Working Group, a newly created body which brings together equipment manufacturers, farm managers and industry representatives to identify best practice guidelines.
Roger Brook, chairman of the Argyll District Salmon Fishery Board and the Rivers and Fisheries Trusts of Scotland, said: "This is yet more proof that escapes, both major and minor, will persist until such time as the companies put the necessary resources into robust equipment and training.
"Escapes are routinely blamed on either predator attacks, causing holes in the cages, or operator error. If the cages are located in open waters to which the natural wildlife of Scotland has access, then they must be capable of withstanding any attack.
"Furthermore, those employed on fish farms must be professionally trained. Time and time again, the salmon farming industry's much-vaunted code of practice to prevent escapes has been shown to be ineffectual. It is becoming ever more evident that the code does not stop escapes – rather it serves to ensure that all the farms operate at the lowest common standard."
Substantial numbers of escaped farmed salmon have been reported in the rivers of Lochaber recently. Jon Gibb, clerk to the Lochaber District Salmon Fishery Board, said: "After 20 years of serial escapes, the industry has proven that it is incapable of containing its fish."