The military has been running free food and drink stalls for the public, they said.
Wesak, denoting the birth of the Buddha, enlightenment or the attaining of the Buddhahood and his death is celebrated among the island's 74 percent majority Sinhala Buddhist community.
Jaffna is the cultural capital of the minority Tamils, who are predominantly of the Hindu religious faith.
After the end of the military conflict between the government troops and Tamil Tiger rebels a year ago, Jaffna had seen a continuous stream of visitors from the south of the island.
Elsewhere in the south in predominantly majority Sinhala community areas the festivities were at a much larger scale.
Buddhist devotees thronged the temples in large numbers from wee hours of the morning.