Myth. Well, this is partially true. According to the American Academy of Family Physicians, pregnant women should not be given vaccines for varicella (chicken pox) or MMR. But the inactivated flu vaccine is safe and even recommended for pregnant women, Dr. Brown says. During pregnancy, women's immune systems are compromised, making them more susceptible to infection. But many are not getting the flu shot; the CDC says that, at last estimate, only 11 percent of pregnant women got one. Dr. Brown says the shot triggers the mother's antibody production, protecting her baby through the first six months of life.