The vaccine provides protection from measles, mumps and rubella.
The police are investigating the deaths as the Ministry of Health conducts its own inquiry.
The Director General of Health, Leausa Take Naseri, said the vaccination programme had been called off until the completion of the investigations.
"We have requested a forensic autopsy, post-mortem on the two babies because it's a police case. It's now also a very different case in the health field," he said.
"We need to look at the cause. We need to find out if the drug was maintained at the appropriate levels."
The nurses who vaccinated the infants have been removed from Safotu for their own safety, Dr Naseri said.
"We're also concerned for the safety of our workers especially the nurses who were involved because it's now easily blamed - the finger is pointed towards the nurses," he said.
In a statement, Prime Minister Tuila'epa Sa'ilele Malielegaoi, extended condolences to the grieving parents.