Hassan Ammar/AF
The Commission of the Promotion of Virtue and the Prevention of Vice, known unofficially as Mutawaa, based its warning on a religious edict from the top committee of Saudi clerics banning such celebrations, the newspaper said.
Saudi Arabia follows the Muslim lunar calendar, unlike all other Gulf states that use the Gregorian calendar.
Members of the commission enforce the kingdom's rule of strict segregation between sexes, and have traditionally forced women to cover from head to toe when in public.
They also go around shops to make sure they are shuttered during prayer times.
The religious police have been accused of abusing their powers.
But since January last year, the religious police have become more discreet with the appointment of their new chief, cleric Abdulatif bin Abdulaziz al-Sheikh, who banned the use of unmarked cars.
Mutawaa also traditionally banned the sale of red roses and gifts for Valentine's Day on February 14.