The Church of the Multiplication at Tabgha, on the shores of the Sea of Galilee, is where many Christians believe Jesus fed the 5,000 in the miracle of the five loaves and two fish.
"Several Jewish suspects have been arrested for the burning of the church and the Nazareth court has decided to extend their detention for the purposes of the investigation," police spokeswoman Luba Samri said on Sunday in a statement on the overnight arrests.
Another police spokesman told the AFP news agency the arrests followed an undercover investigation also involving internal security services.
Benjamin Netanyahu, Israel's prime minister, ordered the domestic intelligence service Shin Bet to find the culprits, as speculation mounted the attack threatened to strain Israel's ties with the Vatican.
The arson had sparked widespread condemnation and concern from Christians globally, with the site visited by about 5,000 people each day.
The number of attacks on Christian and Islamic holy sites has increased significantly over the past few years.
