The North's Western Sector Command on Sunday warned residents of five islands to "evacuate to safe areas" before what it said was the scheduled start time of the military exercise on Monday morning.
The military said Seoul's government "should not forget the lesson" of the North's bombardment of Yeonpyeong Island in November 2010.
"Once the group of traitors starts a reckless military provocation...the KPA (Korean People's Army) will promptly make merciless retaliatory strikes," the North Korean military said.
South Korea's Joint Chiefs of Staff said he was checking whether any such firing drill was scheduled for Monday.
South Korean media last week reported the United States and South Korean navies would stage a joint anti-submarine drill in the Yellow Sea from Monday to Friday.
There was no official confirmation of the joint measure.
The US and South Korea have conducted numerous massive joint sea and air drills in waters east of the Korean Peninsula.
In November 2010, Seoul and Pyongyang exchanged artillery fire in the Yellow Sea border island of Yeonpyeong. The fighting left four South Koreans, including two civilians, dead. Each side blames the other for initiating the clash.