The new devices will have plastic light-emitting diode (OLED) panels, the company said at a Galaxy Note 3 launch event in Seoul.
"We plan to introduce a smartphone with a curved display in South Korea in October," said DJ Lee, Samsung's head of strategic marketing for mobile.
But he revealed no further details.
Digital display technology is progressing towards curved, bendy and foldable screens.
In January, Samsung exhibited prototype products with bendy and extendable screens, but doubts remain as to how such technology can be mass-produced cheaply and reliably.
"A curved screen isn't going to radically change the user's experience of a smartphone, but it does help Samsung differentiate itself in a crowded market where most phones are homogenous, flat-screen rectangles," Ben Wood, analyst at research company CCS Insight, told the BBC.
Samsung launched the Galaxy Gear "smartwatch" and Galaxy Note 3 on 4 September "My understanding is that these new phones will form part of Samsung's Active range, so the curved screen is probably to do with making the phone more flexible and rugged," he added.
Curved displays already feature in large-screen TVs, such as those produced by Samsung and its Korean rival, LG Electronics.
On Wednesday, LG launched a 55in (140cm) curved OLED TV in the UK.
Samsung has also been moving into wearable technology, such as its Galaxy Gear wristwatch phone.
Smartphones are now the dominant type of phone, with CCS Insight expecting one billion to be sold in 2013 out of a total of 1.7 billion mobile phones.