As with other recent phones, all of the sensitive information on the Samsung phone is protected by a fingerprint sensor, which is intended to ensure that only the owner can unlock the phone.
But a technical issue means that anyone can get into the phone when it has a third-party screen protector on it.
The technology giant said it would issue a software patch to fix the issue.
The flaw was first spotted by a British woman who found her husband was able to unlock the phone using his thumbprint when the device was covered with an unofficial screen protector she had bought online.
In a statement, Samsung said: "We are investigating this issue and will be deploying a software patch soon.
"We encourage any customers with questions or who need support downloading the latest software to contact us directly at 0330 000 0333."
The company encouraged customers to use only Samsung-endorsed accessories for their devices.
The fingerprint scanner on the Galaxy S10 is ultrasonic and embedded into the phone's screen, using ultrasonic pulses to detect the 3D ridges of a fingerprint to recognise the user.
First reported by The Sun, Lisa Neilson said she could unlock the phone with a fingerprint not previously registered on the device when using the Â£2.70 screen protector she had bought online.
According to the report her husband was also able to unlock the phone with both his thumbprints, and the flaw also appeared when the same case was fitted to a relative's Samsung device.
Mrs Neilson described the issue as a "real concern".
Biometric scanners such as fingerprint and facial recognition systems have become increasingly popular on smartphones because they are seen as less vulnerable and harder to discover or copy than passwords or number-based unlock codes.