In the following link you can download all shape files and raster datasets for your study area...
http://hydrosheds.org/
In addition, by using ALOS-30m DEM and ArcHydro in GIS you can extract streams network for your location. I attached a file that describes How can you download high resolution DEMs, such as ALOS-30m, SRTM-30m and SRTM-90m...
Thanks for your kind response. Actually, I downloaded Africa shapefile but I failed to clip or extract by mask the Blue Nile basin. Can anyone kindly tell me how to clip the basin from Africa shapefile?
If you have the shape file, select the Blue Nile basin shape and there should be an active option in ArcGIS TOC (table of content) to save the selection as a separate shape file. You can also use query functions to auto select all required attributes. Finally, extract the selected file to save and use for required purpose.