The $3.5 billion pipeline will run from landlocked Uganda's oilfields in the country's west to a port on Tanzania's Indian Ocean coast, but has drawn criticism from environmentalists and European Union lawmakers.
France's TotalEnergies, the lead developer of the pipeline, is facing mounting pressure to drop the project or re-route it because of protests over potential harm to the environment and livelihoods of local communities.
The Cairo-based lender's Chief Executive Officer Benedict Oramah said Afreximbank would contribute towards the pipeline's financing during a meeting Uganda's President Yoweri Museveni, according to a statement released by the presidency.
Oramah said Afreximbank was "willing and considering financing" an oil refinery in the country, according to the presidency.
The EU parliament, echoing campaigns by local and international environmentalists, passed a resolution last month urging TotalEnergies to delay development of the pipeline by a year to explore an alternative route or alternative renewable energy projects.
The EU warned that the pipeline and associated infrastructure would displace about 100,000 people, jeopardise water resources and endanger protected marine areas in Tanzania.
Museveni has reacted angrily to the resolution, calling the EU lawmakers insufferable.
Museveni's government has said it is pursuing efforts to develop both an export pipeline and a domestic crude refinery to help create jobs and maximise benefits from the oil resource.
(Reporting by Elias Biryabarema; Editing by Hereward Holland and Aurora Ellis)