The vandals torched an annexe of the seminary near the walls of the Old City and scrawled "graffiti insulting Jesus", police spokeswoman Luba Samri said, describing it as a "nationalist" attack.
Police said the assailants set fire to the toilet and shower block at the seminary, causing damage but no injuries.
Israeli President Reuven Rivlin condemned the attack.
"It is inconceivable that an act like this could happen in a house of prayer. This is a heinous crime, there must be an investigation and those responsible must be brought to justice," his office quoted him as saying in a phone call to Greek Orthodox Patriarch Theophilos III.
"Such criminals not only threaten to set fire to places of worship holy to all of us, but ignite the regional powder keg upon which we all sit," he added.
Israel's foreign ministry said it expected the police to bring the perpetrators to justice.
"We condemn any action of religious intolerance of any kind," it said in a statement.
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"The government of Israel is committed to protecting the rights and freedoms of all its citizens, regardless of race, creed, or beliefs."
The attack took place just outside the Old City walls on Mount Zion, close to Dormition Abbey, a Roman Catholic institution which was targeted by an arson attack during a visit by Pope Francis last May.
Following a police request, a gag order has been imposed on all details of the investigation which will remain in force until March 4.
Jerusalem Mayor Nir Barkat condemned the attack as "deplorable" and pledged to bring the perpetrators to justice.
On Wednesday, a mosque near Bethlehem in the southern West Bank was set alight and anti-Arab slogans in Hebrew sprayed on a nearby wall.
Palestinian chief negotiator Saeb Erakat denounced the perpetrators of both incidents as "terrorists", blaming Israel's government for inciting the attacks by continuing its "illegal occupation and colonisation based on distorted religious claims."
The United Nations has warned such incidents could "inflame an already volatile environment."
Both incidents bore the hallmarks of so-called "price tag" attacks -- a euphemism for nationalist-motivated hate crimes by Jewish extremists, which generally target Palestinians or Arab Israelis but have increasingly also hit Christian and Muslim places of worship.