The Arsenal Supporters' Trust have voted not to sell their shares to Stan Kroenke as the club is "too important to be owned by one person".
Kroenke secured a controlling stake in Arsenal on Monday and the American businessman is now obliged to make a mandatory cash offer for the remaining shares.
Arsenal's board has recommended all shareholders accept the offer, priced at £11,750 per share, but the AST "unanimously" decided not to relinquish their involvement in the club's ownership structure.
The supporters added they were encouraged to hear that Russian businessman Alisher Usmanov plans to keep hold of his 27% stake.
More than 100 members met in London on Monday night to discuss the proposed takeover and an AST spokesman said: "Arsenal is too important to be owned by any one person.
"The AST wants to work with Stan Kroenke to keep Arsenal supporters involved in the club's ownership structure.
"The AST and the Arsenal Fanshare scheme will not be selling the shares it owns and urges all supporters to reject this offer.
"In just six months the Arsenal Fanshare scheme has gained 1800 members who have invested £500,000 in Arsenal shares.
"This scheme has been widely praised across the football community and is supported by the Government who are currently reviewing football's governance structures.
"AST is encouraged to hear Red & White plan to keep their shares. They have previously stated their long-term commitment to the club and this decision would be a good demonstration of that."
The AST is not against Kroenke's takeover but their support is strongly dependent on the retention of fan involvement in the ownership of the club.
The supporters were certainly encouraged by Kroenke's confirmation that his takeover bid will not be financed by debt secured against the club.
AST officials met with Arsenal chief executive Ivan Gazidis on Monday and received assurances that Kroenke recognises the importance of a supporters' stake in the club.
"The Arsenal board supported Arsenal Fanshare and Stan Kroenke was a member of the board at the time," said the AST spokesman.
"Stan Kroenke has also previously told the AST that he sees supporter shareholders making an important contribution to the club and that the AST provides 'independent perspective to the shareholders, board and management'.
"The AST spoke to Ivan Gazidis on Monday, April 11 and he reiterated the importance he places upon fans' involvement in the club and stated his commitment to custodianship.
"The AST is encouraged that Kroenke's offer states that he does not intend to 'de-list' Arsenal from the PLUS markets.
"In the next few days we will seek further confirmation of his plans in this area and would like to see more detail on this subject in the formal KSE offer document."