The company, which is due to release full-year results tomorrow, said Mr Cohen left the group over "management differences" and "the future direction of the company". He had been chief executive since November 1994.
A spokesman declined to comment further on the row, but pointed to the poor performance of the company's French subsidiary, L'Amy, the spectacle frames and sunglasses manufacturer it acquired in 1994.
Mr Cohen's resignation follows the departure in January of finance director Julian Steadman and non-executive director Warren Kanders. Recently appointed finance director Alan Cox is to assume responsibility for Eyecare UK.
Last year, Mr Cohen received a salary of pounds 152,000, with bonus and benefits lifting his take-home pay to pounds 229,000. He was on a one-year contract and is expected to receive one year's salary as compensation for loss of office.
In January he bought 150,000 shares in Eyecare for pounds 19,500, prompting speculation that the group was on the verge of better times following a profits warning in December.
In addition to owning L'Amy, Eyecare imports sunglasses and reading glasses for distribution to UK high street retailers.
It ran into difficulties last year because of the weakness of L'Amy spectacle sales in France.
Rowan Simmonds, head of small companies at Eyecare's brokers, Credit Lyonnais Laing, said: "They are having a very difficult time in France.
"L'Amy is not making enough frames for designer brands because it is very difficult for it do so commercially in France. It is up against some very efficient Italian competition. They need more brands." L'Amy already supplies Lacoste and Chevingon spectacles.
Last September Eyecare released disappointing interim results showing pre-tax profits down slightly from pounds 2.5m to pounds 2.4m on sales up pounds 1m to pounds 35m. Earnings per share were down from 3p to 2.3p.
At that time it forecast increased full-year sales. However, sales did not pick up and in December it warned that profits would be less than pounds 1m, instead of an expected pounds 3.5m. It blamed the weakness of the economy in France, which accounts for 40 per cent of the group's turnover, and a declining market for house brands such as L'Amy world-wide.
Credit Lyonnais are forecasting profits of pounds 800,000 for 1996, against pounds 3.2m in 1995.
Eyecare had pinned its hopes on a deal agreed last November with Lantis, the US eyewear group, to distribute glasses for DKNY, Donna Karen and Reebok.
The shares closed down 0.25p yesterday at 13p.