Kerr's injury came early last week, with the team set to leave for Sri Lanka on Thursday. Speaking about the timing of the injury, New Zealand's head coach Ben Sawyer said, "Picking up an injury so close to departure for a tour is always disappointing.
"Jess has been working really hard over the winter," Sawyer said. "We were excited to see how she would perform in new conditions for her, but we're confident she will be back fit and ready for our next challenge after Sri Lanka."
"Leigh has had a challenging 18 months since the World Cup but has always been a player that has been on our radar," Sawyer said.
"She's been kept out of the side given the form of Fran (Jonas) and Eden (Carson) who've been performing consistently well and those spin positions have probably been the most hotly contested in our team."
But unlike Kerr, Kasperek will benefit from the spin-friendly conditions in Asia. Sawyer sees that as an upside that will bolster their existing resources.
"With Leigh, Fran, Eden and Melie (Amelia Kerr) we have strong depth in our spin-bowling stocks, and ultimately that's the level of depth we want to get to in all positions.
"Leigh brings a wealth of international experience to the group and I'm sure she will thrive in the Sri Lankan conditions if given an opportunity."
New Zealand's tour will start on June 27 with the first of three ODIs in Galle. The games then will shift to Colombo for three T20Is to cap off the tour.