The council earlier this week warned that any doctor spreading misinformation about the virus and vaccines could lose their job and the right to practice medicine.
About 40 health professionals, mostly doctors, signed an open letter in April opposing the vaccine over safety concerns. The letter names the doctors and provides their Medical Council registration numbers.
RNZ has attempted to contact the doctors who signed the open letter.
Medical Council chair Dr Curtis Walker said a small number of doctors were peddling conspiracies.
The council said on Monday, 13 notifications - or complaints from the public - have been referred to an independent professional conduct committee for further investigation.
It said an unspecified number of complaints do relate to the open letter and some include instances of multiple complaints about the same doctor.
But whether those notifications now mean the committee is set to review all of the medical staff who signed the letter remains unclear.
When asked what steps it was taking against the letter signers, Walker said in a statement privacy legislation prevented it from commenting on any matters under investigation.
He said the council was taking the matter "very seriously' and it did not need to wait for a single complaint to take action.
"It is open to Council to review a doctor's compliance with its standards whenever it has reason to consider a doctor is failing to do so," he said.
No place for anti-vaccination messages - Medical Council
The Medical Council said the expert medical advice and scientific evidence strongly supported that the Covid-19 vaccination was safe, effective and necessary to overcome the global pandemic.
Dr Walker said doctors have a professional duty to provide advice based on evidence.
"There's a mountain of evidence out there of how effective and safe the Covid vaccine is.
"And we've already seen the alternative of unvaccinated populations where millions have died."
The Medical Council said as a regulator it respected an individual's right to have their own opinions.
But it said there was no place for anti-vaccination messages in professional health practice, nor any promotion of anti-vaccination claims including on social media and advertising by health practitioners.
Royal College of General Practitioners president Dr Samantha Murton said while people could choose not to get vaccinated there were serious consequences if the virus breached the borders.
The independent body would decide if charges should be laid with the Health Practitioners Disciplinary Tribunal.
People with concerns about their doctor can contact the Medical Council; and general Covid-19 misinformation or scams can be reported to CERT NZ's website.
RNZ made multiple attempts to contact the doctors who signed the open letter asking them if they have been contacted by the Medical Council, and if they were worried they could lose their jobs.
Dr Mike Godfrey said he retired 13 years ago so was not at risk of losing his licence to practice, and had not been contacted by the Medical Council.
Other than Godfrey, only a small number of the other doctors responded, none answered RNZ's questions or wanted to be named or interviewed.
