They were discovered in "underground chambers " during an excavation of the site in Tuam in County Galway by a commission set up to investigate alleged abuse at such homes.
The Commission of Investigation into Mother and Baby Homes said: "The Commission is shocked by this discovery and is continuing its investigation into who was responsible for the disposal of human remains in this way.
A number of samples from the remains - which were between 35 foetal weeks and two-three years - are likely to date to the 1950s.
A coroner has been informed.
Ireland's Children's Minister, Katherine Zappone TD, said: "It was not unexpected as there were claims about human remains on the site over the last number of years.
"Up to now we had rumours. Now we have confirmation that the remains are there, and that they date back to the time of the mother and baby home, which operated in Tuam from 1925 to 1961."
The commission was set up two years ago to investigate high mortality rates, burial practices, vaccine trials, and secret and illegal adoptions at state-sanctioned religious-run mother and baby homes in Ireland during the 20th century.
It came about after significant international attention was given to the Sister of the Bon Secours home in Tuam, where the remains of nearly 800 infants are thought to be buried.
Joan Burton, Labour Party TD, said: "It now appears as though these children were interred in some kind of mass grave, possibly without normal funeral rights, and maybe even without their wider families having been made aware.
"There have also been allegations that there may have been similar instances with other mother and baby homes around the country.
"I believe the government should resource the commission so that all such allegations can be included.
"It is now incumbent upon the Catholic Church to assist in whatever way they can, so that the truth should be set out in relation to these matters."