Police are investigating after a group of people handing out anti-vaccine flyers approached healthcare workers outside the Craigavon vaccine centre.
The flyers contained misinformation about the contents of the vaccine.
One of those attending the clinic said they felt "very intimidated" after being approached.
The Department of Health said "those who insist on peddling disinformation are doing nothing to advance our efforts to defeat this virus".
BBC News NI understands that a small group of anti-vaccine campaigners assembled outside the South Lake Leisure Centre in Craigavon on Sunday afternoon.
The council-run leisure centre is being used as a vaccine centre for staff within the Southern Trust area.
"Armagh City, Banbridge and Craigavon Borough Council and the Southern Health and Social Care Trust are aware of this matter, which is currently being investigated by the PSNI," the council said.
'False and not helpful'
Patricia Donnelly, the head of NI's vaccination programme, described what had been happening as "unfortunate".
"This kind of misinformation is incredibly unhelpful - anyone who has been called forward for the vaccine needs to have it," she told Stormont's press conference on Wednesday.
Health Minister Robin Swann said those involved in issuing anti-vaccine flyers would be "in complete breach of the Covid regulations".
"They're putting themselves and others in danger," he said.
"I've no problem with free speech in opposition to many things I do or say, but leaflets they're distributing are false and not helpful."
Speaking on the BBC's Good Morning Ulster programme, Dr Gillian Clarke, a senior medical adviser with the Health and Social Care Board, encouraged people to get the vaccine.
"I am aware of the information circulating on social media but I would encourage everyone to get their information from the official channels," she said.
"I would encourage you to attend and if you have any concerns you can talk them over with your vaccinator and I'm sure they will be able to allay any of your fears."
A spokesperson for the PSNI said: "Police received a report in relation to an incident at a vaccination clinic in the Craigavon area and the matter is currently under investigation."