Anti-Christian graffiti was daubed on the Church of the Dormition, one of Jerusalem's leading pilgrimage sites, early on Friday, an AFP correspondent witnessed.
Police said they suspected Jewish religious extremists of spraying the Hebrew-language insults at the site, where tradition says the Virgin Mary died.
"The attack, suspected to be nationalistically motivated, was discovered on the wall of the Dormition Church in the Old City, and the tyres of cars nearby were slashed," police Micky Rosenfeld told AFP.
The words "price tag" and "Christians are apes" were scrawled in Hebrew on the walls of the church, Rosenfeld said, adding police were investigating the incident.
An AFP correspondent said "Jesus is a monkey" was also written on the door to the adjacent cemetery, part of the church complex.
"Price tag" is a euphemism for revenge hate crimes by Israeli extremists, which normally target Palestinians and Arabs.
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Initially carried out in retaliation for state moves to dismantle unauthorised settler outposts, they have become increasingly unrelated to any specific government measures.
The attacks tend to involve the vandalism or destruction of Palestinian property and have included multiple arson attacks on cars, mosques and olive trees.
Perpetrators are rarely caught.
At first, the attacks were predominantly in the West Bank, but they have expanded over time to include sites inside Israel and in Jerusalem, where a number of Christian sites have been targeted.
In December, vandals sprayed anti-Christian graffiti on Jerusalem's Monastery of the Cross and at an Armenian cemetery, in an apparent price tag attack by Jewish extremists.
On May 13, vandals believed to be Jewish extremists desecrated graves and damaged property in a West Bank village in an apparent revenge attack for the stabbing death of Eviatar Borovsky by a Palestinian in April.
Following Borovsky's killing, settlers went on the rampage, stoning Palestinian vehicles in the northern West Bank, including a school bus carrying children.
They also smashed windows of a mosque and set fire to Palestinian farmland.