The five million figure is far less impressive than Samsung's statement yesterday that it has shipped 10 million Galaxy S4 smartphones in less than a month.
However, the global launch of the HTC One was delayed due to a shortage of components including camera lenses.
According to The Wall Street Journal, who cited an anonymous HTC executive, the company "has sold around 5 million One smartphones" since its launch about a month ago.
"Orders are pretty good so far and are still more than what we can supply. This is partly due to the shortage of components. When the issue is resolved next month, we will have a better idea if it’s doing really well or not."
The One shipment news follows the departure of multiple HTC senior executives. Earlier this week, HTC's Chief Product Officer Kouji Kodera left the company, while the vice president of global communications, Jason Gordon, and the CEO of HTC Asia, Lennard Hoornick, also departed.
US website The Verge has also revealed that HTC's global retail marketing manager, Rebecca Rowland, director of digital marketing, John Starkweather, and product strategy manager, Eric Lin have all recently left the company.