Och-Ziff agreed to sell a 9.9% stake to Dubai International Capital in October.
Dubai Holding, owned by the emirate's ruler, on Tuesday said it had taken a $1.26 billion loan from investment bank Morgan Stanley to pay for the acquisition of a stake in a US hedge fund.
Och-Ziff Capital Management in October said it had agreed to sell a 9.9% stake to Dubai Holding subsidiary Dubai International Capital (DIC) for up to the loan amount.
The loan is a short-term bridge loan, Dubai Holding said in a statement, without giving further details.
DIC is the international investment arm of Dubai Holding, and focuses primarily on private equity. Its portfolio includes a stake in European plane-maker Airbus' parent EADS.