"The recovery from the ankle operation will mean Guptill will miss the Bangladesh tour with a possible return for the tour to Sri Lanka in November," New Zealand Cricket (NZC) said in a statement.
The right-handed top-order batsman also fractured a bone in his right little finger while playing in the Caribbean Premier League, the NZC added.
"Since arriving back in New Zealand, specialists have advised Guptill that he will not require surgery but the finger needs to be immobilised in a splint," the statement said.
"A full recovery is expected within three to five weeks."
New Zealand will play two tests, three one-day internationals and a Twenty20 match in Bangladesh.