The distant Type Ia supernovae data compiled by Perlmutter et al. are used to analyze the Cardassian expansion scenario, which was recently proposed by Freese & Lewis as an alternative to a cosmological constant (or more generally a dark energy component) in explaining the currently accelerating universe. We show that the allowed intervals for n and zeq, the two parameters of the Cardassian model, will give rise to a universe with a very low matter density, which can hardly be reconciled with the current value derived from the measurements of the cosmic microwave background anisotropy and galaxy clusters (cluster baryon fraction). As a result, this Cardassian expansion proposal does not seem to survive the magnitude-redshift test for the present Type Ia supernovae data, unless the universe contains primarily baryonic matter.