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.
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.