A civilian militia member travelling with Kashim Shettima said jihadist fighters staged an ambush near the town of Dikwa at about 6:30 pm (1730 GMT) on Tuesday.
The area, near the town of Gamboru and the border with Cameroon, is a known area of activity of the Boko Haram faction loyal to long-time leader Abubakar Shekau.
Shettima, who is stepping down as governor after a maximum of two four-year terms, has been campaigning for a seat in the Senate in elections on Saturday.
He was travelling with the governorship candidate for the All Progressives Congress (APC) party, Babagana Umaru.
Both escaped unhurt and were able to continue to Gamboru, where they spent the night before returning to the state capital, Maiduguri, on Wednesday.
There was no immediate comment from either but a member of the Civilian Joint Task Force said the attack targeted the tail end of the convoy after Shettima had passed.
"There was heavy fighting between the attackers and the soldiers and CJTF," he told AFP on condition of anonymity for security reasons.
"Many vehicles managed to turn back, however two soldiers were killed and two other civilians. An unknown number of party supporters were kidnapped along with their vehicle. The bus they were travelling in got stuck in the sand while the driver was trying to manoeuvre and turn back towards Dikwa."
"All the people in the bus were rounded up and taken into the bush. Another truck belonging to CJTF, which also got stuck, was taken away but the occupants were able to flee." Ngari Kalla, an APC supporter who was also part of the convoy, corroborated the account and said the victims' bodies were taken to Maiduguri.
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