Refugees load a truck in Goris on September 26, 2023, before leaving to Yerevan. AFP
The state border service said Ruben Vardanyan, a businessman who headed the Armenian separatist government from November 2022 until February, had been handed to officials in Baku after being detained on the road to Armenia.
It also released a photograph of Vardanyan, who was born in 1968, being flanked by two security officers, who were holding him by the arms.
Azerbaijan has agreed to allow separatists who lay down their weapons to leave for Armenia under the terms of a ceasefire deal reached last Wednesday.
But an Azerbaijani government source told AFP that border guards were also looking for "war crime" suspects who had to face prosecution.
It was not immediately clear what charges Vardanyan might potentially face.
Azerbaijan has been negotiating "reintegration" terms with separatist leaders in closed-door talks brokered by Russia.
Vardanyan's wife, Veronika Zonabend, said her husband was "arrested and detained by the Azerbaijani authorities at the border this morning as he tried to leave with thousands of Armenians."
"I ask for your prayers and support for my husband's safe release," she wrote her husband's account on the X platform, formerly known as Twitter.
Meanwhile, Armenia said Wednesday that more than a third of Nagorno-Karabakh's population has fled the enclave since Azerbaijan crushed the rebels' decades-long fight for an independent state last week.
Yerevan's attempts to absorb the sea of homeless and hungry ethnic Armenians come with officials still trying to identify the whereabouts of more than 100 people reported missing in a fuel depot blast Monday that claimed 68 lives.
The fireball erupted as refugees from the rebel enclave of Azerbaijan were stocking up on fuel for the long drive along the lone mountain road leading to Armenia.
The Armenian government said 42,500 refugees had entered since Azerbaijan lifted its nine-month blockade on the enclave on Sunday.
It added that nearly five thousand more were already en route.
That represents over a third of the region's estimated 120,000 population and marks a fundamental shift in ethnic control of lands that had been disputed by mostly Christian Armenians and predominantly Muslim Azerbaijanis for the past century.
It also adds to the economic strains of Armenia -- a landlocked Caucasus country with few natural resources and emerging problems in its longstanding diplomatic and military partnership with Russia.