New Zealand Cricket (NZC) said Guptill, who sustained a grade one hamstring strain on his left leg while running between the wickets in the third One-Day International (ODI) in Nelson on Saturday, will take two to four weeks to recover completely.
However, New Zealand coach Mike Hesson said he was positive the explosive right-hander will be fit before the Chappell-Hadlee Trophy against Australia, starting on January 30 in Auckland.
"Martin's obviously a key player for us with the white ball, so to lose him is disappointing," Hesson was quoted as saying by espncricinfo.
"We're confident with some rest, followed by a couple of domestic games, he'll be ready to play a big role against Australia at the end of January."
Hesson said that Broom was an automatic replacement, given his current form in limited overs cricket.
"We needed to replace an attacking opening batsman and with Neil's experience opening in the T20 format and his current form, he was a readymade replacement. Martin also leads our fielding in white-ball cricket and so we're expecting Neil to be a big contributor in that area as well," he said.