The announcement was made by the Burmese (Myanmar) Muslim Association in Yangon, formerly Rangoon, The Irrawadday reported.
Buddhist-Muslim violence has again gripped Myanmar's western Arakan state, also called Rakhine state, home to most the country's minority Rohingya Muslims. It was not year clear what triggered the current wave, which comes five months after similar violence in May.
"Our brothers and sisters are being murdered and their villages are being burned down. ... It is for this reason that we will not celebrate Eid," Myo Latt, a senior BMA leader, told The Irrawaddy.
Eid al-Adha, an important Muslim holiday, is celebrated at the end of the Hajj, the annual pilgrimage to Mecca.
Myo Latt said association members always gather in Yangon for a grand dinner to mark the holy day but this time they have decided against it.
He also said five Muslim organizations had sent a letter to Myanmar President Thein Sein seeking protection for Muslims, but so far had received no reply, the report said.
The BBC reported authorities imposed an overnight curfew in two towns.
At least three people have died since Sunday, and more than 400 houses, a monastery and a mosque have been torched, CNN reported, quoting authorities. Speaking to the Voice of America, al-Haji Nyunt Maung Shein, chairman of the Islamic Religious Affairs Council, said the council has received reports that as many as 178 deaths, Buddhists and Muslims.
Unrest between the Muslims and the majority Buddhists erupted last May following reports of the rape and murder of a Buddhist woman.
Since May, several Rohingya families have sought to move to neighboring Bangladesh, whose government says there already are several thousand Rohingyas in the country.