There were no casualties, but the western part of Assumption Cathedral as well as the priest's housing was damaged.
The pastor of parish, Father Ignatius Rai, said the incident happened at 3 a.m.
The parish released a statement condemning the arson: "The Catholic Church has been involved in social work for half a decade now and will continue with our work despite the frequent attacks."
This is the second time Assumption Cathedral was attacked. It was bombed in 2009 which killed three people and injured 15. A Hindu extremist group was arrested in connection with the bombing a year later.
A former parish priest of the Assumption Cathedral, Fr Silas Bogati, told Vatican Radio: 'We are panicking.
"Nobody left anything in the church premise this time so we don't know whether it was a personal attack or by some disgruntled organisation".
The attack comes weeks before Nepal's first local elections in 20 years on May 14.
The election is believed to be a step to enforcing the country's new secular constitution passed in 2015. However, the Rastriya Prajatantra Party is campaigning against the idea and is working to establish a Hindu state.
Fr Bogati told Vatican Radio: "We are eagerly looking forward to the upcoming local elections in the country and we are in the process with the government.
"This incident, if politically motivated will not harm the peaceful environment in the country."
According to the Nepal Catholic Directory, there are approximately 8,000 Catholics in the country. Nepal has a population of 28 million and 80 percent are Hindu.