No arrests have been made and no injuries were reported.
The incident related to a disagreement between a staff member and a person attending the clinic, who had attempted to take something from the staff member, the police spokeswoman said.
The person left the clinic before police arrived.
Police were continuing to make inquiries about the incident, she said.
Police would not confirm if the person involved in the incident had been denied a Covid-19 vaccine, referring the query to the CDHB. The CDHB would not answer the query either, saying “as the police inquiries are continuing it’s not appropriate for us to provide any further detail at this time”.