There are no known side effects of having mulberries during pregnancy. However, no studies were found that concluded that mulberries are safe or good to have during pregnancy either. Moreover, some women are also allergic to mulberries. Hence, it is recommended that you consult with your doctor before including mulberries in your pregnancy diet.

Taking common medicines during pregnancy, a summary of NHS UK guidelines
You should definitely check with your doctor before taking any medication during pregnancy. Even for medication you were already on at the time of getting pregnant, now needs to be approved by your doctors as