Dananjaya risks a one-year suspension if he fails the procedural biomechanics assessment that he is expected to undergo in the next 12 days.
He played a pivotal role in Sri Lanka's six-wicket triumph, picking up a five-wicket haul in the first innings to stem New Zealand's progress and help tame the opposition to an ordinary total.
He was subsequently suspended the next month for having an elbow extension going beyond the permitted 15 degrees' limit.
He was then cleared to bowl earlier this year following a remodeled action and participated in the ODI series against Bangladesh recently.
Dananjaya's absence, in the event of a one-year ban, could prove to be detrimental to Sri Lanka's Test prospects given the fact that six of their forthcoming five-day games will be played in Asia.
Meanwhile, Williamson rolled his arm for three overs of part-time off-spin in the first Test immediately causing the umpires to doubt the legality of his action.
While Williamson is not expected to fulfill much bowling duties, the two will be allowed to continue bowling until their biomechanic tests are conducted - a positive development for the hosts heading into the next Test match.
The New Zealand skipper has previously been banned from bowling in international cricket in 2014 but later returned to bowl after his new action was approved by the authorities.