The city Department of Health said the babies, all two to six months old, received the shots at the Yen Son Commune medical center in Quoc Oai District, and were transferred to the Saint Paul Hospital to be monitored.
They are in stable condition though some have fever and other common post-vaccination side effects.
It is not known yet how the error occurred and what dosages they got.
District authorities have ordered the suspension of the personnel involved.
Hanoi has not given children Covid vaccines yet though the Ministry of Health has approved the vaccination of those aged 12-17.
The Pfizer vaccine has been given to children in the age group in Ho Chi Minh City, Da Nang and several provinces in recent days.