"In an act that contravenes all laws and customs of war and international humanitarian law, the Ethiopian army executed seven Sudanese soldiers and a citizen who were their captives," the Sudanese armed forces said late Sunday.
The army said "this treacherous act will not pass", vowing to respond to "this cowardly behaviour".
Tensions have risen in recent years, sparking sporadic armed clashes, over the Al-Fashaqa border strip which is close to Ethiopia's restive Tigray region.
There was no immediate response from Ethiopia.
A Sudanese military official who requested anonymity told AFP the soldiers were detained from a border area close to Al-Fashaqa.
Sudan's foreign ministry said it "will immediately recall its ambassador to Ethiopia for consultations" and lodge a complaint with the UN Security Council.
"The Ethiopian ambassador to Khartoum will also be summoned to inform him of Sudan's condemnation of this inhumane behaviour," the ministry said.
Army chief Abdel Fattah al-Burhan visited sites in Al-Fashaqa on Monday, and instructed soldiers "to not allow any new movements or encroachments on Sudanese lands and against its citizens".
Relations between Khartoum and Addis Ababa have soured over Al-Fashaqa, a fertile strip long cultivated by Ethiopian farmers but claimed by Sudan, sparking sporadic deadly clashes between the Sudanese and Ethiopian sides.
Tensions were heightened further after fighting erupted in Tigray in November 2020, sending tens of thousands of refugees fleeing into Sudan.
Khartoum and Addis Ababa have since been locked in a tense war of words, trading accusations of violence and territorial violations.
The border dispute feeds into wider tensions in the region, including over Ethiopia's controversial Blue Nile dam.
Sudan and Egypt, both downstream countries, have been opposed to the Great Ethiopian Renaissance Dam and pushed for an agreement on the filling of its reservoir and the operation of the dam.
In February, Khartoum and Cairo slammed Addis Ababa for unilaterally deciding to start power generation at the dam.
Sudan has been roiled by economic and political turmoil since Burhan led a military coup last year that upended a transition to civilian rule installed following the 2019 ouster of president Omar al-Bashir.