The official said on Thursday the forces came under fire on Wednesday on their way to verify fighting in the village of Edwa on a road between the capitals of North and South Darfur states.
The United Nations said it had confirmed reports the fighting was between the government and the rebel Sudan Liberation Army (SLA).
Jean Baptiste Natama, a senior AU protocol officer, could not say which side had hit the AU officer.
"A Chadian member of the team was shot in the right shoulder. The officer sustained minor injuries. After they were fired on, they returned from the place," he said.
It was the first time an AU soldier had been wounded in the Darfur mission, but not the first time the force had come under fire, Natama said.
The AU force's main job is monitoring the ceasefire agreed in April which both sides accuse the other of breaking. But their mandate also allows them to protect civilians threatened with immediate harm.
"A Chadian member of the team was shot in the right shoulder. The officer sustained minor injuries. After they were fired on, they returned from the place"
Jean Baptiste Natama,
Senior AU Protocol Officer
There are about 1000 AU ceasefire monitors on the ground, and the force is due to grow to more than 3300.
The AU said on Wednesday it would boost its peace-monitoring operation in Darfur with the deployment of 196 Senegalese troops next week. Troops from Tanzania, Gambia and South Africa would also follow, it added.
Some 70,000 people have been killed and more than 1.6 million displaced in Darfur since war broke out in the western part of Sudan in February last year, when rebels rose up against Khartoum, accusing the government of marginalising their region.
The resulting war has provoked what the UN has described as the world's current worst humanitarian crisis.