It is unknown whether or not hypochondria (illness anxiety disorder or health anxiety) is genetic, or runs in families (MagariƱos et al., 2002). To date, no studies have been performed to look into this question of hypochondria running in families.
Reference:
Epidemiology and treatment of hypochondriasis. MagariƱos M, Zafar U, Nissenson K, Blanco C. CNS Drugs. 2002;16(1):9-22.