The US hedge fund is aiming to raise about $1.1 billion in an upcoming flotation but has agreed to sell the shares to Dubai International Capital (DIC).
The private-equity group is owned by the ruler of Dubai and will purchase a minority holding, according to reports in the Times.
Meanwhile, the Carlyle Group and Apollo Management, two other US investment funds, have sold stakes backed by the government of Abu Dhabi.
US firms have been looking to the area for investment ever since Blackstone sold part of its company to the Chinese government.
The move by DIC is good news for Dubai as it looks to involve itself in the international private equity scene and has previously bought stakes in Madame Tussauds and Doncasters.
Executive chairman and chief executive of DIC, Sameer al-Ansari, told the newspaper: "We hold Och-Ziff in very high regard both as a sophisticated investor and a prominent alternative asset manager."