Earlier reports from doctors at the Al-Ahli Hospital in Gaza City said two women had been killed following the raid.
The strike on Thursday damaged the Holy Family Church, the only Catholic Church inside the Palestinian enclave.
"The Holy Family Church in Gaza has been struck by a raid this morning. There are several injuries in the place, including the Parish Priest, Father Gabriel Romanelli," the Patriarchate said in a statement.
"Currently there are no fatalities confirmed. The church sustained damage."
The Vatican did not immediately respond to a request for comment.
The Israeli Defence Forces said it was looking into the matter.
The church was sheltering both Christians and Muslims, including a number of children with disabilities, according to Fadel Naem, acting director of Al-Ahli Hospital, which received the wounded.
At least two people were in critical condition, and others injured included one child with disabilities, two women, and an elderly person, Naem said.
Romanelli was very close with the late Pope Francis and the two spoke often during the war in Gaza.
According to Italy's ANSA news agency, he suffered light leg injuries.
Italian Prime Minister Giorgia Meloni blamed Israel for the attack.
"The attacks against the civilian population that Israel has been carrying out for months are unacceptable. No military action can justify such an attitude," she said in a statement.
In the last 18 months of his life, Francis would often call the lone Catholic Church in the Gaza Strip to see how people huddled inside were coping with a devastating war.
At least two people were killed in strikes on Gaza on Thursday, including one in Gaza City and one in central Gaza's Bureij refugee camp, according to local hospitals.
The war began with Hamas's cross-border attack on October 7, 2023.
That day, militants killed some 1200 people, mostly civilians, and abducted 251 people, most of whom have since been released in ceasefire agreements or other deals.
Fifty hostages are still being held, less than half of them believed to be alive.
Israel's retaliatory offensive has killed more than 58,000 Palestinians, according to Gaza's health ministry, which has said women and children make up more than half of the dead.
with AP
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