The Ethiopian forces had been forced to retreat from the Umm Barakit area, a military statement said, without giving further details, Reuters reported.
The head of Sudan's military, General Abdel Fattah al-Burhan, told reporters the incident took place on Saturday. He said it showed how the military was protecting the country in the wake of a coup attempt in Khartoum last week.
Colonel Getnet Adane, Ethiopia's military spokesperson, did not immediately respond to the request for comment.
Tensions along the border between Sudan and Ethiopia have escalated since the outbreak of a conflict in Ethiopia's northern Tigray region last year that sent tens of thousands of refugees into eastern Sudan.
The tensions have focussed on an area of fertile farmland known as al-Fashqa, where the border is disputed.
ZZ/PR