The unnamed woman discovered she was expecting in December after undergoing treatment at a fertility clinic in Rome, Italy.
But when she was three months along, doctors realised they had mistakenly implanted the wrong embryos, meaning the twins growing in her womb were the biological children of another couple receiving treatment at the clinic.
Four couples received treatment on the day the mistake happened. It is not clear if any of the other women are carrying the wrong baby.
Italy's Health Ministry is investigating mistake and all embryo implantations at the clinic have been suspended until further notice.