Malcolm Ranjith has raised his concerns in a letter, sent to church officials, in which he claims to have received ''foreign information'' that another strike is imminent.
The archbishop of Colombo has been an outspoken critic of the Sri Lankan government's apparent failure to act on Indian government intelligence ahead of the Easter attack.
In his missive, which has been posted on social media, he states a church or another church institution is likely to be targeted.
He states that he has therefore made the decision for churches and Catholic schools throughout Sri Lanka to be closed and public congregations for Mass will be cancelled "until further notice".
"For your own good, we have decided to close down those institutions," he wrote.
More than 250 people were killed, including eight Britons and a further 300 injured during the Easter Sunday bloodshed in the country's capital Colombo.
The terror bombings targeted three churches, packed with worshippers, and three upmarket hotels.
Church spokesman Rev. Edmund Thilakaratne confirmed the authenticity of the letter to The Associated Press but declined to disclose further details, including the source of the foreign information.
An Islamic State-linked group of Sri Lankan nationals is believed to have carried out the co-ordinated suicide bombings.
With suspects still at large the Sri Lankan government introduced a ban on face veils this week designed, it was stated, to help police in their hunt.
A warning was also issued of jihadis in military uniform.
Last week, Muslims were told to stay home for Friday prayers and all of Sri Lanka's Catholic churches were closed.
Instead of the usual Sunday Mass, Ranjith delivered a homily before clergy and national leaders at his residence that was broadcast on television.
Sri Lanka's Muslim leaders, however, were encouraging Muslims to return to mosques for Friday prayers, according to N.M. Ameen, president of the Muslim Council of Sri Lanka.
Ameen said the security situation seemed to have improved, though the group had asked the government for additional protection.
Officials have warned that suspects linked to the bombings are still at large.
Intelligence warnings have indicated Sri Lankan government ministers could be targeted by the same group, which pledged its loyalty to Islamic State militants.
Sri Lankan police have released the names and photographs of nine alleged suicide bombers who carried out the Easter attacks, all belonging to an offshoot of a local group called National Towheed Jamaat.
They included extremist preacher Mohamed Zahran, also known as Zahran Hashim, who was described as the attack leader, and the wife of another suicide bomber, who blew herself up, along with her children and three police officers, at a villa belonging to her father-in-law, who is a prominent spice trader.
The bodies of 10 suspected militants killed in a gun battle with security forces and subsequent explosion at a safe house in Sri Lanka's Eastern province last week were buried without any religious rites.
Police suspect that Zahran's father and two brothers, Rilwan and Sheini, were among the 16 killed at the safe house, according to spokesman Ruwan Gunasekara.
Zahran's wife and daughter sustained injuries from the blast, but their medical condition was not immediately clear.