Emmanuel Igunza
BBC Africa, Nairobi
The authorities have denied permission for him to leave the country to get treatment.
Habtamu Ayelew was arrested in July 2014 and charged with terrorism for allegedly working with banned opposition group Ginbot 7.
His family says he was tortured while in detention and refused access to medical treatment causing his health to deteriorate.
Even though a high court ruling acquitted him of the charges, the prosecution is appealing against that decision.
The 18 exiled journalists on hunger strike say Mr Habtamu will likely not survive if he does not get proper treatment.