The gunmen killed three people who were with Archbishop Paulos Faraj Rahho, said Iraqi Brig. Gen. Khalid Abdul Sattar, a spokesman for the Ninevah province police.
It was not known who was behind the kidnapping, said an aide to Iraq's Cardinal Emmanuel III Delly, leader of the church.
"This act of abduction against a Christian clergy member will increase our fears and worries about the situation of Christians in Iraq," said Archbishop Andreos Abouna.
The Chaldean church is an Eastern-rite denomination that recognizes the authority of the pope and is aligned with the Roman Catholic Church. The Vatican said in a statement the fact that the gunmen knew Rahho had been celebrating a religious rite indicated the kidnapping was premeditated.
Pope Benedict XVI asked the church "to unite in fervent prayer so that reason and humanity prevail among the authors of the kidnapping, and that Monsignor Rahho is returned quickly to the care of his flock," the statement said.
Rabban al-Qas, the bishop of the northern Iraqi cities of Irbil and Amadiyah, said the church was especially concerned because Rahho, 65, has health problems. He did not elaborate.
"This abduction is one in the series of kidnappings carried out by terrorist groups against the Christians," al-Qas said.
Last year's International Religious Freedom Report from the U.S. State Department noted that Chaldean Catholics comprise a tiny minority of the Iraqi population, but are the largest group among the less than 1 million Christians in mostly Muslim Iraq.
Since the U.S.-led invasion in 2003, Iraqi Christians have been targeted by Islamic extremists who label them "crusaders" loyal to U.S. troops. Churches, priests and business owned by Christians have been attacked by Islamic militants and many have fled the country.
Iraq's Prime Minister Nouri al-Maliki pledged last fall to protect and support the Christian minority.
Though most of Iraq has witnessed a decrease of violence over the past six months, the U.S. military regards Mosul as the last urban stronghold of al Qaeda in Iraq, and is engaged in a campaign with Iraqi forces to root out extremists from the city 225 miles northwest of Baghdad.
In an interview with AsiaNews, a Vatican-affiliated missionary news agency, in November, Rahho said the situation in Mosul was not improving and "religious persecution is more noticeable than elsewhere because the city is split along religious lines."
"Everyone is suffering from this war irrespective of religious affiliation, but in Mosul Christians face starker choices," he told the news agency.