The delegation includes Bishop Andudu Adam Elnail and Muslim MP Amar Amoun Deldoum.
Sudan’s Southern Kordofan and Blue Nile states are embroiled in a devastating conflict that has seen bombing by both sides of civilian areas.
The Sudan Armed Forces has reportedly increased aerial bombing since the end of the rainy season, with targets including busy market places.
Mr Deldoum said: “We have only a very small window of opportunity to save tens of thousands of lives. After months of fighting and a poor harvest there is a real risk of famine. African leaders and other countries with influence over Khartoum must insist that humanitarian aid be allowed in immediately.”
Bishop Elnail said: “The civilian population of Southern Kordofan and Blue Nile has been subject to unconscionable violence and unimaginable human rights violations.
"Mosques and churches have been attacked and many lives have been lost. But rather than dividing the people, these attacks have served to further unify the many faiths that have always peacefully coexisted in these areas.
"The African Union has a moral duty to do all it can to restore peace.”
The delegation will meet with ambassadors to the African Union to highlight concerns about civilians and the potential for the conflict to undermine peace between Sudan and South Sudan.
Also making the visit to Ethiopia are Benjamin Barnaba Arne, a Christian representative of the Sudan Council of Churches, and Shara Josep Lago, a Muslim human rights activist from Blue Nile.
Mr Arne said: “The humanitarian crisis in Southern Kordofan and Blue Nile is getting worse. The civilian population– Muslim and Christian alike - are hungry and frightened.
"They have been driven from their homes by violence and are now staring down the barrel of a famine. African leaders have done much already to try to bring peace to Sudan and its neighbours.
"We welcome their efforts but implore them to do more to help end the suffering in the ‘Two Areas’.”
Shara Josep Lago said: “This conflict could undo the fragile peace between Sudan and South Sudan and fuel regional instability. Welcome progress has been made in other areas of the negotiations but the situation in Southern Kordofan and Blue Nile is getting worse.
"Many people are suffering, including women and children: the silent voices of this struggle. The AU must make ending the conflict in the ‘Two Areas’ a priority: it is as important for lasting peace within and between Sudan and South Sudan as oil.”