The rival nations are embroiled in soaring tensions over North Korea's claim that South Korea flew drones over its territory.
Destroying the roads would be in line with leader Kim Jong-un's push to cut off ties with South Korea and formally cement it as his country's principal enemy.
South Korea's military said it was observing various activities in North Korea that appeared to be preparations for demolishing the roads.
"They have installed screens on the road and are working behind those screens, preparing to blow up the roads," Lee Sung Joon, spokesman for South Korea's Joint Chiefs of Staff, told a briefing.
He said the demolitions could be carried out as early as Monday.
Lee said the South Korean military believes the North could also attempt to launch a space rocket, which is viewed by the UN as a banned test of long-range missile technology.
Lee said North Korea may conduct unspecified "small provocations" to ramp up pressure on Seoul.
North Korea recently accused South Korea of launching drones to drop propaganda leaflets over Pyongyang three times in October and threatened to respond with force if it happened again.
In a statement on Sunday, the North's Defence Ministry said the military had issued a preliminary operation order to artillery and other army units near the border with South Korea to "get fully ready to open fire".
A military spokesperson said the entire South Korean territory "might turn into piles of ashes" following the North's powerful attack.
South Korea has refused to confirm whether it sent drones but warned it would sternly punish North Korea if the safety of its citizens is threatened.
North Korea also recently said it will permanently block its border with South Korea and build front-line defence structures to cope with "confrontational hysteria" by South Korean and US forces.
Tensions on the Korean peninsula are at their highest point in years, with North Korea continuing a run of provocative weapons tests and South Korea and the US expanding their military drills.
In January, Kim Jong-un ordered the revision of North Korea's constitution to remove the goal of a peaceful Korean unification, formally designate South Korea as the country's "invariable principal enemy" and define the North's sovereign, territorial sphere.
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