We make an analysis of the isospin symmetry for fragmentation functions assuming isospin symmetry in strong interactions. Taking hadron decay contributions into account, we show that the isospin symmetry is held for unpolarized $\Lambda$ fragmentation functions. Only tiny violations are allowed for the polarized $\Lambda$ fragmentation functions. We show that the recent Belle data on the transverse polarization of $\Lambda$ can be reproduced if the isospin symmetry is kept in the parameterization of the corresponding polarized fragmentation functions. This isospin symmetry can be checked in future SIDIS experiments with different nucleus targets.