Roads in the Troodos area are open to all vehicles on Monday but in some places they may be slippery due to frost.
Police warned in their morning briefing that drivers should be careful as it is possible that the situation may deteriorate due to changing weather conditions.
On Monday the weather will be partly cloudy with some local showers at the west coast and in the mountains. Temperatures will peak at 16C inland, 17 to 18C in coastal regions and 6C in the mountains.
Frost is expected to form in mountainous areas at night.
Temperatures will gradually rise at the weekend.