Samples were given out to reviewers in the US last week and there have been reports of the phone, which costs almost US$2000, breaking or showing bulges or blinking screens.
Samsung had planned media events in Hong Kong and Shanghai this week to unveil the device with which it hopes to revive interest in a flagging smartphone market.
But on Tuesday, the company issued a statement, saying the launch had been put off to an as yet unspecified date.
"While many reviewers shared with us the vast potential they see, some also showed us how the device needs further improvements that could ensure the best possible user experience.
"To fully evaluate this feedback and run further internal tests, we have decided to delay the release of the Galaxy Fold. We plan to announce the release date in the coming weeks."
Regarding the issues that had surfaced, Samsung said: "Initial findings from the inspection of reported issues on the display showed that they could be associated with impact on the top and bottom exposed areas of the hinge. There was also an instance where substances found inside the device affected the display performance.
"We will take measures to strengthen the display protection. We will also enhance the guidance on care and use of the display including the protective layer so that our customers get the most out of their Galaxy Fold.
"We value the trust our customers place in us and they are always our top priority. Samsung is committed to working closely with customers and partners to move the industry forward. We want to thank them for their patience and understanding."
In 2016, Samsung faced a major issue with its Note7 device, with numerous reports of spontaneous combustion. The company was forced to pull the device from sale, in what was seen as a botched response to a serious problem.
And in 2013, Samsung had an issue with washing machines in Australia and was forced to recall something like 150,000 of them. Then, too, the company did not act in time.