To provide a fluorinated elastic copolymer capable of obtaining a crosslinked rubber which is excellent in tensile strength and has a low compression set under high temperature conditions; a method for producing such a fluorinated elastic copolymer; a crosslinked rubber; and a method for producing such a crosslinked rubber. A fluorinated elastic copolymer having structural units based, respectively, on monomers (a), (b) and (c), and further having iodine atoms. Monomer (a): at least one member selected from the group consisting of tetrafluoroethylene, hexafluoropropylene, vinylidene fluoride, chlorotrifluoroethylene and perfluoro(alkyl vinyl ether). Monomer (b): at least one member selected from the group consisting of compounds represented by formula (I): CR1R2═CR3—R4—CR5═CR6R7 (I) (wherein R1, R2, R3, R5, R6 and R7 are each independently a hydrogen atom, a fluorine atom or a methyl group; and R4 is a C1-10 perfluoroalkylene group which may have an etheric oxygen atom inserted between carbon atoms). Monomer (c): at least one member selected from the group consisting of ethylene and propylene.