Zambia, who have had a steady diet of warm-up games in preparation for the defence of their title, called off a friendly with Namibia in Nelspruit on Tuesday.
"They have cited a strenuous schedule as the reason for the cancellation," Namibia Football Association president John Muinjo said.
"Their coach wants the final week before the Nations Cup to be used as a winding down period."
Zambia have lost to both Tanzania and Angola and drawn with Morocco in three friendlies over the last three weeks. They play Norway at home in Ndola on Saturday.
They begin the Nations Cup with a Group C match against Ethiopia in Nelspruit on January 21.