Using data from the Sloan Digital Sky Supernova Survey-II (SDSS-II SN Survey), we measure the rate of Type Ia supernovae (SNe Ia) as a function of galaxy properties at intermediate redshift. A sample of 342 SNe Ia with 0.05 < z < 0.25 is constructed. Using broadband photometry and redshifts, we use the PÉGASE.2 spectral energy distributions to estimate host galaxy stellar masses and recent star formation rates (SFRs). We find that the rate of SNe Ia per unit stellar mass is significantly higher (by a factor of ~30) in highly star-forming galaxies compared to passive galaxies. When parameterizing the SN Ia rate (SNRIa) based on host galaxy properties, we find that the rate of SNe Ia in passive galaxies is not linearly proportional to the stellar mass; instead an SNRIa∝M 0.68 is favored. However, such a parameterization does not describe the observed SNRIa in star-forming galaxies. The SNRIa in star-forming galaxies is well fitted by SNRIa = (0.41 ± 0.15) × 10–10 M 0.72 ± 0.15 + (0.65 ± 0.25) × 10–3SFR1.01 ± 0.22 (statistical errors only), where M is the host galaxy stellar mass (in M ☉) and SFR is the SFR (in M ☉ yr–1). We show that our results, for SNe Ia in passive galaxies, are consistent with those at higher redshifts (favoring SNRIa∝M) when accounting for the difference in the ages of our galaxies. This suggests that the rate of SNe Ia is correlated with the age of the stellar population. The MLCS extinction parameter, AV , is similar in passive and moderately star-forming galaxies, but we find indications that it is smaller, on average, in highly star-forming galaxies. This result appears to be driven by a deficit of the reddest (AV > 0.15) SNe Ia in highly star-forming galaxies. We consider that the high levels of dust in these systems may be obscuring the reddest and faintest SNe Ia.