Martin will be replaced for the Tests later this month by Mark Gillespie, who is already in Bangladesh for the one-day series starting on Thursday.
New Zealand selector Dion Nash said Martin was making a good recovery but had lost condition in recent weeks.
"With such a big season ahead, it would have been foolish to rush Chris back too early," Nash said.
"He is better at home working on his fitness and strength and preparing himself for the two-Test series against Australia next month," he said.
Martin was earlier ruled out of the three one-day internationals against Bangladesh due to the injury, which cut short his season at English county Warwickshire.