Indonesia Monday began re-inoculating children who received fake vaccines in a major drug counterfeiting scandal that has sparked protests from concerned parents.

President Joko Widodo attended a health clinic in Jakarta at which 36 children were given fresh booster vaccines, vowing the process would continue until all youngsters affected had received new shots.

The health ministry said the first stage of re-inoculation would take place at four hospitals and clinics on the main island of Java where children had been identified as having received fake vaccines.

Police last month smashed a criminal syndicate accused of selling fake vaccines for more than a decade to health clinics across Indonesia, a vast archipelago of 255 million people.

Twenty-three people, including midwives and doctors, have been arrested for alleged involvement in the scheme and vaccines have been confiscated from dozens of health centres across the country.

One of the midwives at the clinic visited by Widodo on Monday is suspected of involvement in the scam, the president said.

The scandal sparked panic and anger among Indonesian families, who last week rallied outside hospitals demanding answers about their children's health.

Widodo urged concerned parents to remain calm and give authorities time as they assess the scale of the problem, suggesting reforms could be needed in future to protect the community.

"This gives us all momentum to improve governance around the pharmaceutical industry regarding the manufacture and distribution of medicines, including vaccines," Widodo told reporters.

"Our goal is for the entire community to receive good health care."

The syndicate, which police said operated for more than a decade, manufactured and distributed fake boosters for diseases including tuberculosis, hepatitis B and tetanus.

The scandal was brought to light after a major pharmaceutical company alerted Indonesian authorities that some of its products had been counterfeited.