The Cupertino-based firm opened pre-orders shortly after midnight Pacific time (8am in the UK), and within just an hour the US website indicated that shipping times had slipped from the expected delivery date of September 21.
Those making later pre-orders were told that their handsets would instead ship in two weeks.
An Apple spokesperson did not comment on the report.
The UK Apple store website says that buyers of the 32GB model face a wait of "2-3 weeks", while the 16GB and 64GB versions will be dispatched in two weeks.
Despite the iPhone 5 being the most expensive Apple smartphone ever, at £529 for the base model, it appears that consumer demand is massive for the product, which was unveiled by Apple on Wednesday (September 12).
Its predecessor the iPhone 4S took 22 hours to sell out its initial pre-order stock in the US, while the iPhone 4 took 20 hours. But the iPhone 5 seemingly took just 60 minutes to achieve that feat.
Copyright: AppleThe phone comes with a larger 4-inch screen, improved camera technology, a zippier A6 processor, support for superfast LTE connectivity and a new connector and headphones.
Apple intends to ship initial pre-orders and start in-store sales of the iPhone 5 in nine countries, including the US and UK, on September 21.
In the firm's most aggressive rollout pattern ever, the smartphone will be available in 100 countries by the end of the year.
Apple is expected to shift around 6 million handsets in the opening weekend of iPhone 5 sales, and could sell a staggering 10m in the first week.