"We are looking at two weeks, anything before is a bonus," Bangladesh coach Chandika Hathurusingha told reporters on Wednesday.
"He's been one of the form batters as well as wicketkeeper in all formats, but injuries are part and parcel of the game."
Rahim's injury cleared the decks for reserve wicketkeeper Nurul Hasan's one-day debut in the second match at Nelson on Thursday.
Beginning on Jan 3, Bangladesh play three Twenty20 matches in New Zealand followed by tests at Wellington (Jan. 12-16) and Christchurch (Jan 20-24).
(Reporting by Amlan Chakraborty in New Delhi; editing by Nick Mulvenney)
