The arson had sparked widespread condemnation and concern from Christians globally, with the site visited by some 5,000 people each day.
"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 in a statement of the overnight arrests.
Police did not provide a number, but an ultra-nationalist organisation said three young Jews had been arrested.
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.
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One of the buildings within the compound was completely destroyed in the blaze but the church itself was not damaged.
Hebrew graffiti was found on another building within the complex, reading "Idols will be cast out" or destroyed. The text is part of a common Jewish prayer.
There has been a long line of attacks on Christian and Muslim holy places in both Israel and the West Bank in which the perpetrators are believed to have been Jewish extremists.
In the immediate wake of last month's attack, police had detained 16 young Jewish settlers, but they were later released without charge after providing statements.
Ten of those initially detained were from Yitzhar, a Jewish settlement in the West Bank which is known as a bastion of extremists and where some residents have been involved in previous hate crimes.
In April, vandals smashed gravestones at a Maronite Christian cemetery near Israel's northern border with Lebanon.