Williamson, averaging 88.58 in Tests in 2015, took a nasty blow to the hand in the first innings of New Zealand's first-Test victory, where he scored 88 and 71 and became only the fifth player to pass 1,000 Test runs this year.
Ahead of the second and final Test in Hamilton, which starts on Friday, Williamson described his injury as "part and parcel" of cricket and said he would not seek treatment during the series.
"It's part and parcel of cricket I suppose. You get a few knocks on the fingers and when it doesn't get hit it settles a little bit and gets a bit less sensitive."
Williamson said New Zealand will keep their winning combination for the second Test after being presented with another green-top wicket in Hamilton.
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With conditions ripe for seam and swing bowling, New Zealand ruled out bringing in an extra spinner and opted to maintain their four-pronged pace attack.
"We're playing the same (line-up) as the last match, with the look of the surface we will go in with that extra seamer," Williamson said, suggesting New Zealand would likely bowl first if they win the toss.
"It's green, Dunedin was green, and we just feel it might be more suited to seam bowling."
Their cause was helped by the inexperienced Sri Lankan attack being unable to capitalise on the conditions, but Williamson does not expect New Zealand to get off so lightly this time.
Sri Lanka will not confirm their line-up until just before the game, but captain Angelo Mathews indicated changes were also unlikely.
"The wicket's really green, lots of grass on it, so it's definitely bowl first and if we bowl first we'll look to rectify the mistakes that we did in Dunedin because we were nowhere near our best," he said.
"This will do a lot more than Dunedin, it has a lot more grass and the seamers will come into play.