Ulster Unionist Party (UUP) leader Jon Burrows said it is “extremely concerning” that names were published on Tuesday evening.
Burrows, a former police officer, told the Stephen Nolan Show that 41 officers were named on the NI Courts website.
“It’s out there on WhatsApp. It’s going around virally,” he said.
“Whenever you receive the message now, it says on it, forwarded many times. And we need to find out how that’s happened and what lessons can be learned.”
He has submitted an urgent oral question to the Stormont speaker’s office to discuss the situation on Monday.
Burrows said Justice Minister Naomi Long should explain exactly what happened.
He added: “This latest incident only heightens the need for robust safeguards to protect those who serve and their families.”
The chair of the Police Federation for Northern Ireland, Liam Kelly, said that “publishing the names of officers on the court list appears to be another avoidable and embarrassing error”.
“The list has now been taken down but questions must be asked how this happened,” he added.
Kelly said those mentioned on the court list “deserve answers”.
He added that it is “a matter of considerable concern that claimants’ names have been further published and, like this federation, they will be demanding some clarity and answers”.