Cricket New Zealand said Tuesday the match will be played in Hamilton on December 23 at the start of Bangladesh's tour of New Zealand.
Cyclone Sidr smashed into the southern coastal districts of the delta nation on November 15, killing at least 3,200 people and leaving millions homeless or short of basic staples such as rice.
"With the Bangladesh cricket team touring New Zealand in December and January we felt it is appropriate and the right thing to do to assist the relief efforts in their country," Cricket New Zealand chief executive Justin Vaughan said.
The New Zealand XI will be captained by Stephen Fleming, who was replaced earlier this year as captain of the national team by Daniel Vettori.
An invitational Masters team will also play the New Zealand under-19 side in another Twenty20 game before the main match as part of the fund raising.
Bangladesh will play three one-day internationals and two Tests during their tour of New Zealand.