Italy's health ministry said it was launching an investigation into the mix-up, which was only discovered when the woman was three months pregnant.
The mistake happened on December 4th, when four different couples were receiving treatment at a specialist fertility unit at the Sandro Pertini Hospital in Rome, La Stampa newspaper reported.
It is not clear whether the mistake led to any of the other women becoming pregnant with the wrong baby.
Health Minister Beatrice Lorenzin said on Sunday investigators would look at whether the hospital had "respected all the legal procedures" and expressed concern that she had only learnt about the mistake through press reports.
"The national standards on assisted fertilisation, which are based on European directives, are very rigorous, and if applied correctly, guarantee the traceability of all biological material used in the reproduction process," she said.
The local health authority in Rome said it only became aware there was a problem of "genetic incompatibility" between the parents and the embryos on March 27th.
It said it has halted all embryo implantations at the clinic until further notice.
The investigation will be led by geneticist Giuseppe Novelli and will look into whether there was any further mix-up of the embryos of two of the other women.