The Opposition leader says John Key should have acted sooner to address any potential conflicts of interest involving a Minister whose brother faces child indecency charges.
An injunction prevented media from naming the man or the Cabinet minister concerned.
The man is scheduled to appear in court today.
Andrew Little said the "price of public office" was one sometimes had to step down when an issue such as a case involving the minister's sibling emerged.
"It's not about what the minister has or hasn't done, nor indeed what the minister's sibling has or hasn't done. It's about public confidence in the office of that minister," he told TV One's Breakfast.
Earlier this year, Mr Little stood social development spokeswoman Carmel Sepuloni down from her portfolio when her mother faced welfare fraud charges.
Ms Sepuloni was reinstated after her mother was sentenced.
Mr Little told Breakfast suppression orders now prevented Mr Key from acting, but the Prime Minister should have taken action when he was first alerted to the case weeks ago.