Russian prosecutors are investigating allegations that hospital staff in Yekaterinburg gagged babies because they did not want to hear them crying.
The patient at the hospital in the southern Urals who reported the case heard the children's muffled cries.
She used her mobile phone to film a baby lying in a cot with his mouth taped, while others had dummies taped to their mouths. They are all orphans.
The case, covered widely by Russian media, has caused deep shock.
Russians are used to scandals in the hospital, but this case has touched a raw nerve, says the BBC's Richard Galpin in Moscow.
The patient who reported the incident, Elena Kuritsyna, had been in the hospital with her own children.
Elena Kuritsyna spotted the babies during a visit to the hospital
She said she heard the suppressed crying of young children in the next ward.
"I heard that a baby was mumbling in a neighbouring room; when I looked in, I saw the baby with plaster over his mouth; he could not cry or do anything, was just mumbling," she told Reuters television.
She approached the nurse in the ward and was initially told to mind her own business. Children were crying too loudly, and distracting nurses from their work, she was told.
She eventually persuaded the nurse to remove the plaster, but she says that afterwards the nurse did it again.
The nurse has been suspended and on Wednesday the head doctor at the hospital was reprimanded.
Prosecutors have opened a criminal investigation, and say they have discovered that sticking plaster was used more than once.
"Children in the first year of life were systematically gagged with sticking plaster to make children behave quietly," the prosecutors' press service said.
It is alleged the babies were silenced because there were too few staff to deal with them.