The Chinese technology company revealed the prototype in a post to the social media site Weibo.
It promised the "double-folding" device was coming and asked the public to help name it.
Samsung and the start-up Royole have previously unveiled flexible-screened phones of their own.
But they only folded at a single point.
"It is very interesting that Xiaomi has adopted a three-way folding option on its prototype," said Ben Wood, from the consultancy CCS Insight.
"It is hard to judge the relative benefits of this versus a single fold and it will depend considerably on the user interface that Xiaomi chooses to adopt as it opens the ability to have a three-quarter screen option.
"However, it certainly means there is an additional point of failing. The fold is typically the area where there are most likely to be problems over time."
Rumours of the device's existence began to circulate at the start of the month after the journalist Evan Blass posted a separate video of the handset to Twitter. However, he was unable to verify it was real.
The company has, however, confirmed to the BBC the latest clip, featuring its co-founder Bin Lin, is authentic, but said it had nothing to add at this point.
Weibo shows that the video has already been played nearly 3.5 million times and attracted thousands of comments since it was uploaded on Wednesday.
Foldable screens present smartphone-makers a means to make their products look more distinctive after a period during which they have coalesced around the same form: a dark black rectangle with ever-shrinking bezels.
But the innovation is expected to come at a steep price, at least when the first devices go on sale.
And it is unclear as yet what use cases manufacturers will promote to justify the added cost.
Royole is still seeking feedback from software creators via a "developers' version" of its handset. That went on sale late last year.
Huawei has said it will launch a phone with a fold-out screen in 2019, while Samsung has said it will reveal more details about its plans for the Galaxy X phone - first teased in November - at a press event on 20 February.
Lenovo-owned Motorola has also published a patent that illustrates how a flexible display could be incorporated into its classic flip-open Razr design.
And Google has said it is working on a new version of Android that will natively support "foldable" devices rather than requiring manufacturers to create their own workarounds to adapt to the changing dimensions of their devices' screens.
Other manufacturers may also have further announcements of their own to make at the Mobile World Congress trade show in Barcelona, which begins on 25 February.
"Folding displays are still very much a case of a solution looking for a problem but I remain firmly convinced that we are seeing the seeds being sown for the next generation of smart devices," said Mr Wood.
"[One concern is] the additional bulk the fold creates.
"However, there is no doubt a smartphone with a folding screen will be a magnet for gadget lovers."