Shetland Catch Chairman John Goodlad said Leask, managing director at the firm for 11 years, has not worked since March because of the undisclosed illness.
Leask oversaw strong growth at the firm during his tenure, including a huge expansion of the Lerwick-based processing plant in 2001.
Shetland Catch has faced financial problems over the past year. In September, the company and main rival Fresh Catch were raided by the Scottish Fisheries Protection Agency as part of an illegal fishing investigation.
The company's Shetland Smokehouse subsidiary was forced into bankruptcy in last month, less than two years after it was taken over, the result of record-high raw material prices, the company said.
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