  Primordial magnetic fields generated in the very early universe are one of
the candidates for the origin of magnetic fields observed in galaxy clusters.
After recombination, the Lorentz force acts on the residual ions and electrons
to generate density fluctuations of baryons. Accordingly these fluctuations
induce the early formation of dark halos which cause the Sunyaev-Zel'dovich
(S-Z) effect in cosmic microwave background radiation. This additional S-Z
effect due to primordial magnetic fields amplifies the angular power spectrum
of cosmic microwave temperature anisotropies on small scales. This
amplification depends on the comoving amplitude and the power law index of the
primordial magnetic fields spectrum. Comparing with the small scale CMB
observations, we obtained the constraints on the primordial magnetic fields,
i.e., B < 2.0 nGauss for n=-2.9 or B < 1.0 nGauss for n=-2.6, where B is the
comoving amplitude of magnetic fields at h^-1 Mpc and n is the power law index.
Future S-Z measurements have the potential to give constraints tighter than
those from temperature anisotropies and polarization of cosmic microwave
background induced by the magnetic fields at the recombination epoch.
