Journalists said their handsets were "unusable" 48 hours after receiving them, Sky News reported.
The Galaxy Fold – similar in size to a normal smartphone when closed – opens out to form a tablet-sized device.
Described by the South Korean company as "unlike any device that has come before it", it features six cameras and will cost about £1,500 when it goes on sale next week.
It can be opened and closed 200,000 times – or 100 times a day for five years – Samsung says.
But Bloomberg's Mark Gurman tweeted that the "screen on my Galaxy Fold review unit is completely broken and unusable just two days in".
Under a picture of the device, he added, "Hard to know if this is widespread or not."
Dieter Bohn, from The Verge, said, "Super yikes. Something happened to my Galaxy Fold screen and caused a bulge.
"I don't know how it happened, and I'm waiting to hear back from Samsung. It's broken."
CNBC's Steve Kovach tweeted a video of his screen flickering, writing: "After one day of use..."
Two journalists said they had removed a thin, protective layer from the screens, thinking it was meant to be removed when it was actually supposed to stay on.
But reporters from CNBC and The Verge said they left the layer on and it still broke.
Samsung said it would "thoroughly inspect these units in person to determine the cause of the matter".
It will also be making it clear that the screen's protective layer is necessary to prevent scratches, a spokesman added.
This is not the first time Samsung has experienced a difficult product launch, after the Galaxy Note 7 was recalled because batteries were catching fire.