The unusual move comes after western Norway was whipped by strong winds, causing damage to the huge submerged cage in which 127,000 of the fish are kept by the world's largest salmon producer.
Marine Harvest deployed nets in the surrounding areas in an attempt to catch the two-kilogramme (4.4-pound) swim-aways, but is also offering 500 kroner (60 euros, $80) for each fugitive returned.
The escapees are damaging to the marine ecosystem because the farmed salmon weaken the genetic makeup of their wild cousins if they reproduce with them. Industry professionals have successfully tackled the problem in recent years and have vastly reduced the number of escapees.
Figures from 2012 showed that 38,000 salmon escaped, ten times fewer than in 2011, compared with a peak in 2006 of 921,000, according to the Norwegian Fisheries Directorate.