Hostilities broke out in recent days in Tsemlet, western Tigray, an area claimed by forces from the neighbouring Amhara region.
Flights to Tigray have been suspended since Thursday.
Drones were used extensively during the 2020-2022 Tigray war between the Ethiopian army and forces of the Tigray People's Liberation Front (TPLF) that killed at least 600,000 people, according to African Union estimates.
A truck driver was killed in the first attack in central Tigray, which began at 3:30 am (0030 GMT) and lasted about 30 minutes, Dimtsi Woyane television, a media outlet close to the Tigrayan authorities, reported.
Images posted on Facebook show a a body slumped in the driver's seat.
A second strike in the same area at around 5:30 am (0230 GMT) targeted another truck carrying pepper, the outlet said.
Two sources close to the local authorities confirmed the strikes to AFP.
A spokesperson for Ethiopia's federal army has not responded to AFP requests for comment.
On Friday, the African Union expressed "deep concern over recent developments" in Tigray and urged "all parties to exercise maximum restraint."
Tension has been brewing over the presence of troops from Amhara and the neighbouring country of Eritrea in Tigray, violating a peace deal that ended the war.
Last year, the head of Tigray's interim administration established by Addis Ababa was forced to flee Mekele, the regional capital, amid growing divisions within the TPLF.
The TPLF which controlled all of Ethiopia before being displaced by Prime Minister Abiy Ahmed, remains banned.
Addis Ababa accuses the group of forging ties with neighbouring Eritrea and "actively preparing to wage war against Ethiopia".
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