The first of the three Tests against New Zealand begins on Thursday (February 28).
The 31-year-old played in the final ODI at Dunedin, despite scans revealing a broken rib prior to the game.
Furthermore, Rahim has also suffered a side strain and a wrist injury this tour - the latter being a cause for concern ahead of the series opener in Hamilton.
"He [Mushfiqur] has got a problem with his wrist area, just above his thumb,” Bangladesh head coach Steve Rhodes said.
“The idea is to basically stop that moving so he has got a protection on that which will stop it from moving. We will keep it like that for three days and then we will open it up and see what sort of movement there is and how the pain is and we will take it from there.
“I wouldn't really say he is out or wouldn't really say [he's] in. So, the answer is sorry, I don't know."
Despite injury niggles bothering multiple players in the squad, Rhodes is confident that a fit eleven will take the field at Seddon Park.
"I think that 15 days' cricket, which it could be out of 24 days, is difficult. Not many teams will play a three-Test series in 24 days," Rhodes said. "It is not something to worry about, given that some of the squad are carrying niggling injuries, it could be a factor as the series progresses.
"We got a few little niggles here but hopefully we got a great medical team and they'll pull them through and we will put our best 11 out there."
First Published: February 23, 2019, 10:35 AM IST