AT&T has sold out of the company’s allotment of iPhone 4 preorder units, as first reported by Boy Genius Reports and confirmed by AT&T in a statement. The company’s announcement is specific to AT&T’s own inventories, and not Apple’s or the other retailers offering the device.

The company said in a statement that June 15th “was the busiest online sales day in AT&T history.” Those who did successfully place a preorder sale through AT&T will receive theirs up on June 24th, but as of now, new preorder sales will be received on June 25th “or later.”

AT&T customers will be notified via e-mail when their iPhone 4 order is placed as to when they will receive their order. The company also said there will be additional inventory available on a first-come, first-served basis.

In the meanwhile, you can try to preorder through Apple’s Web site — a process that is still failing as of this writing — or use Apple’s new Apple Store app for the iPhone to place a reservation for an iPhone 4. Note that reservations are different from preorders. With a reservation, Apple will hold an iPhone 4 for you for pickup on June 24th. With a preorder, you tender credit card information at the time of the preorder.