In September, the firm confirmed it was in the early stages of assessing an offer for the Premier League club.
But in a statement issued to the London Stock Exchange, the company said it had "terminated" its interest in a takeover bid and was "no longer considering making an offer".
Cain Hoy had until 10 October to firm up its interest or withdraw it.
Spurs are currently trying to finance a project to construct a new 56,250-capacity stadium.
When Cain Hoy confirmed their interest in a Tottenham takeover on 12 September, without the club's consent, Spurs swiftly issued a statement saying they had met company representatives but added there were "no ongoing discussions".
Instead, the club said it was focused on the new stadium development and the season ahead.
When contacted by BBC Sport regarding Cain Hoy's withdrawal of interest, the club said it had nothing further to add.
Cain Hoy's latest statement, however, did leave open the prospect of the company renewing its interest after a six-month restriction, which comes into place with immediate effect in accordance with the City Code on Takeovers and Mergers.
Tottenham plan to move out of their White Hart Lane stadium by 2017, but a legal wrangle means they will have to find a temporary home venue for the 2017-18 season.
But West Ham would likely block any move from Spurs to ground-share at the Olympic Stadium, according to Hammers' vice-chairman Karren Brady.
Other potential ground-shares include Wembley and Stadium MK in Milton Keynes.
American investment company Cain Hoy has said it is no longer considering making an offer to buy Tottenham.