Customers can select one or two units on its website using a drop-down menu in the "review bag" screen just before checkout.
This compares with the 999 maximum units available for the iPhone 14 and 14 Plus, as well as for older devices.
It is not known whether this measure was in place before it became apparent that demand was exceeding supply, causing a huge shortage.
Apple is facing heightened demand for the latest models of its flagships, particularly the coveted Pro devices, the camera systems of which have been significantly improved.
Although the supply shortage may not come as a surprise, given that delays have been expected all year due to factors such as supply chain issues, parts shortages and inflation, this year might have caught Apple by surprise.
Apple was already dealing with orders that overwhelmed stock. It has been reported that customers buying several iPhones caused an inadvertent shortage, resulting in some people who lined up early ending up empty-handed.
During the start of iPhone 14 sales at The Dubai Mall on September 16, The National reported that one person bought six devices. At least one other news outlet reported that another bought 10 units.
It is not known if Apple puts a cap on how many devices a customer can purchase at its stores.
Another issue facing customers is that delivery times for the iPhone 14 Pro units have been increased to five to six weeks. Apple normally indicates a period of three to four weeks.
In the past, Apple has typically indicated conservative delivery time estimates. However, it has usually beaten those projections, being able to ship the devices earlier than advertised.
The shortage of iPhone 14 units has potential customers considering snapping up their devices from profit-seeking resellers, where prices are inflated.
Listings for these units are continuing to grow. As of about 5pm UAE time on Wednesday, there were more than 600 listings for iPhone 14 units on Dubizzle, one of the biggest platforms for classifieds.
That is up from the more than 500 listings The National spotted on Tuesday.
The highest priced is a Hong Kong version of the deep purple, 1TB iPhone 14 Pro Max, going for Dh11,000.
The iPhone 14 and iPhone 14 Plus models start from $799 (Dh3,399) and $899 (Dh3,799), respectively, while the iPhone 14 Pro costs $999 (Dh4,299) and the iPhone 14 Pro Max starts at $1,099 (Dh4,699).
Curiously, one of the listings that appeared was for an "original condition" iPhone X, the first iPhone without a home button that was launched in 2017.