A consortium led by Oleg Novachuk and KAZ director Vladimir Kim last month offered 640 pence for the 61% of the mining company's shares it doesn't already own to take it private, offering minority shareholders a 12% premium on the previous day's close.
"If successful at the current value and without an increase in price, the offer will prevent the current minority shareholders of Kaz Minerals from realising the full value of their investment," said CFC Management chief executive Ekaterina Chernova.
CFC Management is a Russia-based investment advisor that represents Maxim Vorobyev and other minority shareholders, which jointly control around 3.6% of KAZ's share capital.
"We will advise our clients to vote against the offer," Chernova added.
Reuters reported on Monday that the London-listed miner's fifth-biggest investor RWC Partners also plans to vote against it.
RWC Partners, which runs $9 billion in emerging and frontier markets, owns just under 3.3% of KAZ Minerals.
(Reporting by Clara Denina, editing by Louise Heavens)