Zoe faces a maximum of six months in jail on a charge of resisting arrest stemming from an altercation with police last August.
A conviction could cost the beleaguered MLA his seat in the legislative assembly for a second time. Zoe was forced to step down in 1994 after he was convicted of spousal assault.
Zoe pleaded not guilty to the charge in December, but has declined to discuss the case publicly.
A conviction would trigger a hearing in the legislative assembly, where members could vote to expel Zoe from his seat.
The trial - scheduled to be before a territorial court judge - is the latest in a series of troubles for the North Slave MLA.
Zoe was stripped from his position as minister of municipal and community affairs this summer after an incident at the Royal Canadian Legion, where he reportedly insulted Newfoundlanders.
The trial would have marked the second time in the last week a member of the 15th Legislative Assembly has appeared in a Yellowknife courtroom to face criminal charges.
Former justice minister Roger Allen was convicted of sexual assault on Jan. 19 and sentenced to four months in jail.