Pictures from the Israel Museum showed the marble head of the goddess Athena knocked off its pedestal and a shattered statue of a pagan deity.
Authorities said initial questioning suggested the Jewish tourist, 40, smashed the statues on Thursday because he considered them “to be idolatrous and contrary to the Torah”.
The man's lawyer, Nick Kaufman, denied that he had acted out of religious fanaticism.
He said the man was suffering from a mental disorder that psychiatrists have labelled “Jerusalem syndrome”, a condition said to cause foreign pilgrims to believe they are figures from the Bible.
The condition is believed to be induced by the religious magnetism of a city sacred to Christians, Jews and Muslims.
The man, whose name was not released by officials, has been ordered to undergo a psychiatric evaluation.
The incident took place the day before the end of the Jewish holiday of Sukkot. It has been a turbulent week in Jerusalem, where footage emerged of a group of Christian pilgrims being spat on by a group of ultra-Orthodox Jews.
The museum called the incident a “troubling and unusual event” and said it “condemns all forms of violence and hopes such incidents will not recur.”
The damaged statues were being restored, museum staff said. The museum declined to offer the value of the statues.
“This is a shocking case of the destruction of cultural values,” said Eli Escusido, director of the Israel Antiquities Authority.
“We see with concern the fact that cultural values are being destroyed by religiously motivated extremists.”
The museum opened as usual on Friday morning, about 16 hours after the incident.
The vandalism appeared to be the latest in a series of attacks against historical objects in Jerusalem.
In February, a Jewish-American tourist damaged a statue of Jesus at a Christian pilgrimage site in the Old City, and in January, Jewish teenagers defaced historical Christian tombstones at a prominent Jerusalem cemetery.