The general, whose name was not reported, was with a convoy advancing on Bor when rebels fired on it outside the town, the BBC reported.
No other information on the incident was reported.
The attack came as representatives from the South Sudanese government were scheduled to meet with rebel leaders in Addis Ababa, Ethiopia, to work on a cease-fire agreement.
Negotiations in Ethiopia have been ongoing since Friday, but Sunday was the first time the two sides were to meet face-to-face.
Clashes in South Sudan began Dec. 15 after President Salva Kiir accused former Vice President Riek Machar, who he dismissed in July, of attempting a coup. Machar has denied plotting to overthrow Kiir.
Fighting between government forces and those loyal to Machar has been seen in Bor, as well as in the oil-producing states of Unity and Upper Nile in the north, army spokesman Philip Aguer said.
The conflict has also taken on ethnic undertones, as Kiir is from the Dinka community and Machar from the Nuer group, the BBC said.
So far, at least 1,000 people have been killed and nearly 200,000 displaced in South Sudan.