The transmission of correlated electrons through a domain wall in a ferromagnetic one-dimensional system is studied theoretically in the limit of a domain wall width smaller or comparable to the electron Fermi wavelength. The domain wall gives rise to both potential and spin-dependent scattering of the charge carriers. Using a "poor man's" renormalization group approach for the electron-electron interactions, we obtain the low temperature behavior of the reflection and transmission coefficients. The results show that the low-temperature conductance is governed by the electron correlations, which may suppress charge transport without suppressing spin current. The results may account for a huge magnetoresistance associated with a domain wall in ballistic nanocontacts.