A weekend advisory said members of the community should take necessary precautions as rumors of civil unrest became rife.
It also urged its schools and places of worship to make appropriate arrangements.
Social media posts have threatened civil unrest, starting this week.
But president of the Masjid Ul-Halil Mosque in Lautoka, Abu-Bakr Sadiq Koya, said the community had confidence Fiji's security forces would keep them safe.
He said Muslims in the country would continue to go about their lives as normal.
"Everybody's talking about that something will happen. People are talking about it but I know it is (nonsense) because nobody can do anything with the security," Sadiq Koya said.
"The Fiji government, the military and the police are very strong here in Fiji. It is not so easy for anybody to take any action here."
League president Hafiz-Ud-Din said a mosque and shops in the town of Nausori, outside the capital Suva, were vandalized on Thursday.
He said after the Christchurch terror attacks in New Zealand, the league did not want to take any chances, so the memo was sent out.
Meanwhile, Fiji's security forces have moved to reassure the community that the rumors of civil unrest are unfounded.
Over the weekend about 50 police officers marched through the main streets of Lautoka, the second largest city of Fiji.
The Deputy Secretary for the Ministry of Defense and National Security, Ilai Moceica, denied the march had anything to do with the rumors of civil disturbances.
"There's nothing happening that people should be afraid of," he said.
"The police, the security forces at this time, everything's normal. They've assured the people of Fiji that everything's normal.
"And we can confirm that everything's normal from the Ministry of Defense and National Security."
Moceica said he was unaware of who was behind the rumors.
Earlier, Police told local media the Lautoka march was part of an "operational readiness check" the force was undergoing across the country.
The police march was accompanied by motorcycles and patrol vehicles.
The military said it was working alongside police to ensure the nation's security and safety.
Fiji, a country in the South Pacific, is an archipelago of more than 300 islands.
The Muslims of Fiji comprise approximately 7% of the population. The Muslim community is made up of people of Indian origin, descendants of indentured laborers who were brought to the islands in the late 19th century by the British colonialist rulers of the time.