Anemia and Chemotherapy Chemotherapy can damage your body’s ability to make red blood cells, so body tissues do not get enough oxygen, a condition called anemia. People who have anemia may feel very weak or tired, dizzy, faint, or short of breath, or may feel that their hearts are beating very fast. Bone Marrow Suppression and Chemotherapy Nearly all chemotherapy agents suppress the bone marrow, and that, in turn, causes a reduction in the number of blood cells. This raises the risk for anemia, infection, bleeding, and bruising. Infection and Chemotherapy To reduce your risk for infection, avoid people who are sick with contagious illnesses, including colds, the flu, measles, or chickenpox. Neutropenia: A Vulnerable Time for Infections Neutropenia is a condition in which the body has a very low number of white blood cells. Because white blood cells attack harmful bacteria, viruses, and fungi, neutropenia increases the risk for infections.