New Zealand Cricket confirmed that Henry will take the place of Southee in the T20I squad for the two games against Sri Lanka.
New Zealand’s coach Mike Hesson expressed disappointment at the injury to Southee but stated that the team management will be working hard to ensure his complete recovery.
"Tim was feeling really fresh after coming back from a break for the first two ODIs, so it's certainly disappointing for him that this has happened now," Hesson said.
"Tim's obviously a key member of our team and been a strong performer for us in all three formats, so he's a big loss.
"We haven't set a date for his return at this point, but will continue to monitor him and work to get him back to full fitness as quickly as possible."
The third ODI against Sri Lanka in Nelson was Southee's first game in the format since June 2015 after he was given a rest for the tour of Africa.
In the 2015 Cricket World Cup, Southee played a crucial role by picking 15 wickets from nine matches to complement Trent Boult who had a tournament haul of 22 scalps.
The two-match T20I series between New Zealand and Sri Lanka will get underway with the first game on 7th January in Mount Maunganui while the second game will be played in Auckland on 10th January.
© Cricket World 2016