The South Korean firm dished out the £1,800 folding device to various members of the media to try out and many have shared images of the device being damaged in less than 24 hours.
In a statement, Samsung vowed to "thoroughly inspect" the product to find out what is causing the problem.
They said: "A limited number of early Galaxy Fold samples were provided to media for review. We have received a few reports regarding the main display on the samples provided.
"We will thoroughly inspect these units in person to determine the cause of the matter."
They also warned that a reason for the damage could be due to the fact that the reviewers had removed a "protective" film on the screen, which they said should not be taken off.
They continued: "Separately, a few reviewers reported having removed the top layer of the display causing damage to the screen.
"The main display on the Galaxy Fold features a top protective layer, which is part of the display structure designed to protect the screen from unintended scratches.
"Removing the protective layer or adding adhesives to the main display may cause damage. We will ensure this information is clearly delivered to our customers."