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The decision comes after multiple reports claimed the phone was "exploding" during or after charging. It also comes less than a week before rival Apple releases its brand new iPhone 7 devices.
Samsung will take about two weeks to take to prepare replacement devices.
"In response to recently reported cases of the new Galaxy Note 7, we conducted a thorough investigation and found a battery cell issue," said a Samsung spokesperson at a press conference held in South Korea on Friday.
"To date (as of September 1) there have been 35 cases that have been reported globally and we are currently conducting a thorough inspection with our suppliers to identify possible affected batteries in the market. However, because our customers' safety is an absolute priority at Samsung, we have stopped sales of the Galaxy Note 7.
"For customers who already have Galaxy Note 7 devices, we will voluntarily replace their current device with a new one over the coming weeks. We acknowledge the inconvenience this may cause in the market but this is to ensure that Samsung continues to deliver the highest quality products to our customers. We are working closely with our partners to ensure the replacement experience is as convenient and efficient as possible."
On Wednesday, Samsung said it was delaying shipments of the Note 7 for "quality" testing, but it didn't say exactly what the problems were with the phone.
The Galaxy Note 7 launched in August to glowing reviews. But investors are not reacting well to the news of the battery problems, and the company has lost about $7 billion (£5 billion) in market value this week.