The iPad Mini is shown in San Jose, California. (AP Photo)
"Demand for iPad mini exceeded the initial supply and while many of the pre-orders have been shipped to customers, some are scheduled to be shipped later this month," Apple said.
"We're working hard to build more quickly to meet the incredible demand," CEO Tim Cook said in a statement.
The 7.9-inch iPad mini marks Apple's first foray into the smaller-tablet segment, and is the company's first major new device since the death of co-founder Steve Jobs last year.
Apple shares were up nearly 1 percent at $582.27 in trading before the bell.