The company confirmed that "certain celebrity accounts" had been breached, but claimed the attacks were not down to security weaknesses.
Earlier reports suggested the theft may have been related to a weakness with Apple's Find my iPhone service, called iBrute.
The flaw allowed attackers multiple attempts at cracking a user's Apple password, but has now been fixed. Others speculated on a wider breach of Apple's iCloud storage service, which automatically backs up photos taken on an iPhone.
When we learned of the theft, we were outraged and immediately mobilised Apple’s engineers to discover the source.
But Apple dismissed claims of a wider breach and said hackers had managed to crack the victims' user names, passwords and security questions in a "very targeted" attack. The mystery has left security experts puzzled, with Apple stating its engineers had investigated the issue for more than 40 hours.
Apple said: "When we learned of the theft, we were outraged and immediately mobilised Apple’s engineers to discover the source. Our customers’ privacy and security are of utmost importance to us.
"After more than 40 hours of investigation, we have discovered that certain celebrity accounts were compromised by a very targeted attack on user names, passwords and security questions, a practice that has become all too common on the Internet.
"None of the cases we have investigated has resulted from any breach in any of Apple’s systems including iCloud or Find my iPhone. We are continuing to work with law enforcement to help identify the criminals involved."
The breach came to light after nude photos of the targeted celebrities spread online. A reported 101 victims have been targeted, prompting an FBI investigation.
The incident comes at a tricky time for Apple, since the company is widely expected to unveil the iPhone 6, and other devices, at its US media event next week.