They reported hearing an explosion and seeing a fire overnight.
But the military, which has said there were no casualties, did not acknowledge the incident until seven hours later.
The launch was in response to North Korea firing a missile over Japan early on Tuesday.
This is the first time Pyongyang has flown a missile over Japan since 2017 – and it prompted a show of force from the US, Japan and South Korea which conducted military drills. Seoul and Washington also fired a volley of missiles into the East Sea – also known as the Sea of Japan – between the Korean peninsula and Japan.
The South Korean military later confirmed that one of their missiles failed soon after it was launched and crashed – this was separate to the ones launched with the US.
The military also said that the Hyunmoo-2 missile carried a warhead but that it did not explode, and apologised for causing worry.
Residents in Gangneung said they saw a bright flash and heard an explosion at around 01:00 on Wednesday (16:00 GMT Tuesday).
They were left in the dark for hours, and many of them posted on social media wondering what had happened, while sharing photos and videos of the incident. The footage showed what appeared to be a brightly burning fire, with smoke rising from a distance.
“I can’t sleep because I feel anxious [after hearing] the explosion,” said one user, according to news site Kang Won Ilbo. Another wondered if a plane had crashed.
It's only just been confirmed that the US and ROK conducted their own missile drill in response to North Korea's recent missile test.
One of South Korea's Hyunmoo-2 failed shortly after launch and crashed, but caused no casualties.https://t.co/j7K3semX3g
— Raphael Rashid (@koryodynasty) October 5, 2022North Korea’s missile launch on Tuesday was the fifth carried out by Pyongyang in a week. Many of its missile tests are conducted on a flight path that reaches a high altitude, avoiding flights over its neighbours.
But firing over or past Japan allows North Korean scientists to test missiles under circumstances “that are more representative of the conditions they’d endure in real-world use”, analyst Ankit Panda told news agency Reuters.
In September, North Korea passed a law declaring itself to be a nuclear weapons state, with leader Kim Jong-un ruling out the possibility of talks on de-nuclearisation.
