The Ethiopians came from behind to equalise in the 64th minute through Saladin Seid after Tunisia had taken a fourth-minute lead from a penalty converted by their Swiss-based attacking midfielder Oussama Darragi.
The draw in a warmup international in Qatar, where Tunisia are preparing, came after success for Ethiopia last week at home against Niger, another of the sides who will be competing in this month's continental championship in South Africa.
Ethiopia are playing at the Nations Cup finals for the first time in more than 30 years and remain something of an unknown quantity. They compete in Group C with defending champions Zambia, Nigeria and Burkina Faso.
Tunisia are in Group D with Algeria, Togo and the much fancied Ivory Coast. The tournament starts on January 19.