Police initially said that a security alert was sparked on Hawthorn Street after "a suspect explosive device" was found at a property in the area.
It was later confirmed that officers from the Serious Crime Branch found the military style weapons while conducting the search as part of an investigation into ongoing dissident terrorist activity.
The rocket launcher and the warhead - which, if viable, contains explosives - have been taken away for forensic examinations.
A PSNI spokesperson said: "These weapons systems are clearly intended to kill and we should be in no doubt that the recovery of these items has saved lives."
A number of properties were evacuated, but residents have since been allowed to return to their homes and the road has now reopened.
Earlier this month Gardaí in Co Tipperary intercepted a suspected dissident republican haul of rocket launchers and explosives, which were believed to be en route to Northern Ireland.
There are no further details.