Seven people were charged with stealing and conspiracy to steal a baby from the Komfo Anokye Teaching Hospital earlier in February.
Suwaiba Mumuni, whose baby is among the five missing, told the BBC she believes her child is still alive.
The hospital, the second largest in Ghana, has denied the allegations.
The BBC's Sammy Darko in the capital, Accra, says the case of the missing babies has caused outrage in Ghana.
Youths stormed the hospital in Kumasi, 270km (167 miles) north-west of Accra, on Thursday, temporarily closing the maternity wards, he says.
Ms Mumuni said after she gave birth on 5 February, she was told that her baby was stillborn and it was taken away by attendants.
When her relatives arrived later in the day to collect the body for burial, it could not be found, she said.
"The only news I am expecting to hear is that my baby has been found," Ms Mumuni told the BBC.
"They told me my baby is dead, but they have not been able to produce the body... I am confident my baby is alive."
The bodies of another four babies allegedly delivered stillborn that day are also missing.
"The ministry will leave no stone unturned until the truth is established," Health Minister Sherry Ayittey said in a statement.
Ms Ayittey said the hospital had 14 working days to find the bodies of the babies "for burial by the families".
Staff at the hospital, who spoke on condition of anonymity, said they often felt overwhelmed and there were inadequate resources to deal with demand.
Our reporter says the seven people charged on Thursday over Ms Mumuni's missing baby were given bail.
Ghana's health minister has given a hospital in the city of Kumasi 14 days to produce the bodies of five babies that were allegedly stillborn.