The church at Tabgha is built where Christians believe Jesus performed the miracle of the loaves and fishes, also known as the Feeding of the 5,000.
Hebrew graffiti found on a wall is thought to indicate the attack may have been the work of Jewish extremists.
Police detained 16 teenagers for questioning but later released them.
Spokeswoman Luba Samri told the AFP news agency that they were freed "with no conditions attached, after being interviewed and giving statements".
The BBC's Kevin Connolly in Jerusalem says Tabgha is a sacred site to the many thousands of Christian pilgrims who visit the Holy Land every year.
The arson attack on the Church of the Multiplication of the Loaves and Fishes caused extensive damage to a book shop and other buildings at the complex but did not destroy the 5th Century mosaic floors which are its key archaeological feature.
Two people who had been staying at the complex were also taken to hospital suffering from smoke inhalation.
A verse from a Hebrew prayer denouncing the worship of "idols" was found spray-painted in red on a wall of the church.
Our correspondents say the graffiti will suggest to many that the attack is part of a sporadic campaign by a small group of right-wing Jewish extremists against non-Jewish targets in Israel, but police said it was too early to tell.
"The torching of the church is a cowardly and despicable act which contradicts Israel's basic values," Internal Security Minister Gilad Erdan said in a statement.
The Israeli pressure group, Rabbis for Human Rights, says there have been 43 hate crime attacks on churches, mosques and monasteries in Israel and the occupied West Bank since 2009, Reuters news agency reports.

The measures include the installation of concrete roadside barriers to protect tennis fans outside the venue.
The Met Police says the plans will also see firearms officers in and around the grounds and a mobile unit which can "respond to emerging incidents".
Tournament organisers say there has been a "proportional uplift" in measures introduced in past years.
About 7,000 people were queuing outside the All England Club on the first day of the championships.
Wimbledon said the use of the barriers was part of "enhanced measures" this year and would provide "visible physical security".
They have been placed along the route people take as they make their way to and from the tournament as well as in the public queuing zone.
The Met Police said it "continually develops and refines plans for this type of event and planning has been under way throughout the year".
"We have put together a proportionate policing plan with a significant number of resources to support the club to deliver a really safe, secure competition," said Supt Jo Edwards.
"Our plans are based on a number of factors, including the threat level and recent events in London and the UK."
Vehicles were driven at pedestrians on Westminster Bridge in March, on London Bridge in June and near a Finsbury Park mosque later the same month.
Supt Edwards said officers will be working in uniform and plain clothes during the two-week event.
Police also warned the public against pick-pockets and touts selling unauthorised tickets.
Wimbledon has published security advice on its website, saying there would be extensive searches of people, bags and vehicles and urging spectators to allow plenty of time for entry.
The tennis club has continued its ban on spectators bringing in selfie sticks or any "objects or clothing bearing political statements".
Source: Wimbledon

24 June 2015 Last updated at 14:21 BST
But this is a hoverbike - one of the world's first flying motorcycles, that travels in the air at low levels.
It's makers Malloy Aeronautics say it's based on drone technology and has been developed over many years.
It can be flown by a driver or remotely.
The first version was made in 2011 using a 1200cc BMW motorbike engine.
The latest prototype is powered by four bladed fans.
It's still not clear when the first ones will be ready to buy but there's a lot of interest, including from the US Military.
Watch the hoverbike in action.
Arsonists are believed to have started a fire which has damaged a Roman Catholic church on the Sea of Galilee in northern Israel, police say.
[NEXT_CONCEPT]
Security at Wimbledon is being stepped up after the recent UK terror attacks involving vehicles hitting pedestrians.
[NEXT_CONCEPT]
It's billed as having the simplicity of a motorbike and the freedom of a helicopter.