HPV Vaccine and Pregnancy In every pregnancy, a woman starts out with a 3-5% chance of having a baby with a birth defect. This is called her background risk.This sheet talks about whether exposure the HPV vaccine may increase the risk for birth defects over that background risk.PV Vaccine and Pregnancy In every pregnancy, a woman starts out with a 3-5% chance of having a baby with a birth defect. This is called her background risk.