The kidnapping was reported by Syrian state media and confirmed by a member of the official opposition leadership.
Yohanna Ibrahim is head of the Syriac Orthodox Church in Aleppo and Boulos Yaziji leads the Greek Orthodox Church in the city.
They are the most senior Christian clerics caught up directly in the war.
It was not immediately clear who had kidnapped them.
Christians made up about 10% of the mainly Sunni Muslim country's population before the uprising against President Bashar al-Assad began just over two years ago.
According to the UN, at least 70,000 people have been killed overall in the civil war and more than one million are now living as refugees in neighbouring countries.
State TV announced that an "armed terrorist group" had kidnapped the two bishops as they carried out "humanitarian work in Aleppo countryside".
Abdulahad Steifo, a Syriac member of the opposition Syrian National Coalition, said the men had been kidnapped on the road to Aleppo from the rebel-held Bab al-Hawa crossing, which is close to the Turkish town of Reyhanli.
Asked who was behind their abduction, he said: "All probabilities are open."
Christian residents of Aleppo, speaking on condition of anonymity, told AFP news agency that gunmen had killed the bishops' driver.
In an interview with BBC Arabic's Saeed Shehada a week ago, Bishop Ibrahim said he was optimistic about the future of Christians in Syria:
"There is no persecution of Christians and there is no single plan to kill Christians. Everyone respects Christians. Bullets are random and not targeting the Christians because they are Christians," he said.
Militants in a rebel-held area of northern Syria have abducted two bishops travelling from the Turkish border back to the city of Aleppo.