It did not state the stake's size, but Chief Executive Officer Sameer al-Ansari said last week the firm planned to invest $500 million in an unnamed "Japanese-headquartered company we like very much."
Dubai International said in July it might invest up to $1.5 billion in one or two publicly listed Japanese companies.
A $500 million investment represents almost 1 percent of Sony, whose market value is about $51.3 billion.
Representatives of Dubai International, the international investment arm of government-owned Dubai Holding LLC, and Tokyo-based Sony, the world's No. 2 consumer electronics maker, would not comment on the purchase's timing or financial terms.
A Sony spokesman said Sony was pleased by the investment.
Dubai Holding is controlled by Sheik Mohammed bin Rashid al-Maktoum, who holds holds 99.67 percent of the company.