The foetus, believed to have been between 15 and 20 weeks old, was dumped into the bin after a procedure at Monklands Hospital in Airdrie.
Bosses at NHS Lanarkshire apologised for the incident and said they are carrying out an urgent review to find out exactly what happened.
Scottish Health Minister Alex Neil said: "Clearly something has gone very badly wrong.
"There is a proper procedure and foetuses are stored at Wishaw General Hospital in these circumstances in a very protected and respectable environment."
A spokesman for NHS Lanarkshire said: "We are sorry for the distress caused by this incident.
"We are carrying out a critical incident review as a matter of urgency."
The spokesman said they had special arrangements in place for "sensitive disposal of a foetus".
He added: "Options include a hospital cremation or a private burial or cremation."
A Scottish Government spokeswoman said: "We would expect all NHS staff to follow appropriate procedures in situations such as this which ensure that patients' dignity and privacy are fully respected.
"Any deviation from this would be completely unacceptable."