To provide an epoxy-resin composition and prepreg for producing a fiber-reinforced composite material which exhibits excellent curability and has excellent flame retardance and heat resistance, as well as to provide fiber-reinforced composite materials produced using the prepreg and to provide housing for electronic/electrical devices. The epoxy resin composition contains component (A): a phosphorus compound; component (B): an epoxy resin which has at least three epoxy groups in the molecule, and which does not correspond to component (A) nor include component (A); component (C): an epoxy resin curing agent which does not have a urea structure in the molecule; and component (D): a dimethylurea compound represented by formula (a) (in formula (a), “R” is a hydrogen atom or an alkyl group having any number of 1 to 10 carbons).