Is anemia contagious?

No. It is secondary to the deficiency of iron or some vitamins or some of the genetic or inherited problems.
Usually not... Anemia can be caused by medications, auto-antibodies, iron deficiency (diet issues), bleeding, cancer, and inherited conditions (for example sickle cell disease). The only "contagious" cause i can think of are viruses. Viruses can sometimes transiently suppress the bone marrow's ability to make red blood cells (parvovirus for exmaple, though there are many).