The New Zealand skipper suffered a shoulder injury while fielding in Bangladesh's first innings of the rain-hit Test in Wellington, which New Zealand won comfortably by an innings and 12 runs.
Coach Gary Stead said scans had detected a tear to Williamson's left pectoral minor muscle in his shoulder.
"There's obviously irritation and a wee bit of bleeding, it's not a major injury," Stead said.
"We're hopeful that he will recover quickly, and the thing for us is to make sure he doesn't aggravate it any more. He will come to Christchurch and we will make an assessment there on whether he plays."
With the series already won, Stead said New Zealand would take a ‘safety first’ approach, particularly with this year's World Cup on the horizon.
"No player wants to give up their spot in the Test team. But I think it's safe to say that we will probably err on the conservative side, and if there's any chance of risk then we're likely to pull him from that game."
Williamson had suffered considerable discomfort while batting, although he managed to score 74.
He did not take the field for Bangladesh's second innings with Tim Southee taking over the captaincy duties.
Williamson is due to fly to India after the Bangladesh series to join up with the Sunrisers Hyderabad squad in the cash rich T20 tournament.
"If things progress as we hope, then still going to the IPL shouldn't be a problem to him," said Stead.
"But he's also aware that if he's not quite 100 per cent, then we will potentially hold him back as well and make sure that he is right before he goes on that plane."