Researchers think the cancer cells from the mother crossed the placenta and implanted themselves into the fetus, without being recognized by the developing immune system. They say some of the DNA was missing in the immune system, which kept it from trying to counter the cancer cells.
The baby girl has been under intensive treatment and is said to be doing well.
Despite the case, experts still say the chances of a pregnant woman passing cancer on to an unborn child are very remote.
The report is published online in the Proceedings of the National Academy of Sciences.