Hamish Marshall was picked instead, with coach John Bracewell saying he believed Marshall could handle the move into the Test arena after good results in One-day Internationals.
"Hamish has had previous success in the subcontinent on New Zealand 'A' tours and that experience will be important in the conditions we will be playing in," Bracewell said.
Marshall will bat in the middle order "where he is a different sort of player than the likes of (Scott) Styris and (Nathan) Astle," Bracewell said.
McMillan was likely to rejoin the squad for the One-day series.
The Black Caps will play their first Test in Dhaka from October 19 to 23 and the second in Chittagong from October 26 to 30. They will also play three One-day matches.
The squad: Stephen Fleming (captain), Nathan Astle, Ian Butler, James Franklin, Hamish Marshall, Chris Martin, Brendan McCullum, Kyle Mills, Jacob Oram, Michael Papps, Mark Richardson, Scott Styris, Daniel Vettori and Paul Wiseman.