"The matter has been postponed to October 20. The prosecutor is not feeling well," said magistrate Dambudzo Malunga.
Theo Bronkhorst is facing charges of "failing to prevent an illegal hunt" over the death of the iconic lion, which was killed by American trophy hunter Walter Palmer with a bow and arrow in July.
Bronkhorst has applied to have the case thrown out of court.
Read: Zimbabwean behind Cecil hunt asks for case to be dropped
He reiterated that his papers were in order and said he was optimistic he would be acquitted.
"I don't think I have a case to answer," Bronkhorst, 52, told reporters outside the court in Hwange, adding that he felt "frustrated" by the postponement.
"The Parks (department) checked my papers and they were in order."
The hunt provoked worldwide outrage after it turned out that Cecil was a well-known attraction among visitors to the Hwange National Park and was wearing a tracking collar as part of an Oxford University research project.
Read: Zimbabwe hunter behind Cecil lion killing freed in sable smuggling case
Palmer, a dentist from Minnesota, was hounded on social media over the killing and went into hiding after demonstrations outside his dental practice.
He apologised for killing Cecil, a 13-year-old male renowned for his distinctive black mane, and appeared to blame Bronkhorst for misleading him.
Zimbabwean authorities on Monday dropped plans to seek Palmer's extradition to face charges, saying his papers were in order and that he was misled into believing that the hunt was legal.
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