Williamson injured the shoulder while fielding on Sunday but went onto score 74 in the first innings. However, he twice had to call out the physio for some running repairs and didn't look comfortable playing some shots.
"Kane is obviously keen to play this final game, but we'll look to take a safety-first approach, particularly with the World Cup on the horizon," said head coach Gary Stead after the conclusion of the second Test.
"It's very minor but we're hopeful he will recover quickly. Kane's managed his way through injuries before, he's had niggles all the time, and he seems to find a way through. The extent of this and the unknown of this were the things we were unsure about, but hopefully, he'll get through that fine.
"It's like any muscle, there's obviously irritation and a wee bit of bleeding, it's not a major injury, so we're hopeful in a short period of time, he will be back to full noise. The thing for us over the next 48 to 72 hours is just to make sure he doesn't aggravate it any more."
Stead also said it was an injury that had only been seen five times worldwide.
"It's a pretty rare injury – they've only seen I think five in the world before," he said.
"I know that the physio staff were saying 'We'll make this a case study' because it is so rare."
Stead is confident that Williamson will be fully fit ahead of the IPL, but said New Zealand Cricket (NZC) board won't take any risk if he isn't 100 percent ready.
"From what I've been speaking with the physio and Kane about, if things progress as we hope, then going to the IPL shouldn't be a problem for him. But he's also aware that if he's not quite 100 percent, then we will potentially hold him back as well and make sure he is right before he goes on that plane."
The Black Caps also suffered a further injury blow on the final morning when wicketkeeper BJ Watling strained a hamstring during his warm-up and was replaced by the uncapped substitute Peter Bocock.
"BJ [Watling] has a minor left hamstring strain and we felt it was best he didn't keep today to give him the best chance of being fit for the third Test," said Stead.
NZC will take a call on replacement players for the 13-man squad after the conclusion of the latest round of the Plunket Shield (NZ's domestic red-ball competition). However, Stead hinted that Will Young, who's already a part of the squad, will make his debut if Williamson fails to recover on time.
"Will [Young] has been in our Test squad as batting cover for the past two series and he should be confident following some strong performances domestically and for New Zealand A," Stead said.
With an innings-and-12-run victory in Wellington, New Zealand have already gained an unassailable 2-0 lead in the series. The third Test will be played in Christchurch from March 16.
First Published: March 12, 2019, 7:20 AM IST