Mr Cohen added investors in Magnum were being asked to pay a premium for the Ben & Jerry's brand "because it has such a loyal following".
"As they destroy Ben and Jerry's values, they will destroy that following and they will destroy that brand," he said.
"It'll become just another piece of frozen mush that just going to lose a lot of market share."
A spokesperson for Magnum said Ben & Jerry's was "not for sale" and it had "always respected" the brand's commitment to continue its "social mission".
The demerger of Unilever's ice cream business saw primary shares in Magnum open at €12.20 (£10.66) - down on the expected €12.80 (£11.18) reference price set by the EuroNext exchange in Amsterdam. But it bounced back up by 1.3% at close of trading.
The spin off means Magnum is now the world's biggest standalone ice cream business.