We calculate the nucleosynthesis of proton-rich isotopes in the carbon-deflagration model for Type Ia supernovae (SNe Ia). The seed abundances are obtained by calculating the s-process nucleosynthesis that is expected to occur in the repeating helium shell flashes on the carbon-oxygen (CO) white dwarf (WD) during mass accretion from a binary companion. When the deflagration wave passes through the outer layer of the CO WD, p-nuclei are produced by photodisintegration reactions on s-nuclei in a region where the peak temperature ranges from 1.9 to 3.6x10^9^K. We confirm the sensitivity of the p-process on the initial distribution of s-nuclei. We show that the initial C/O ratio in the WD does not affect much the yield of p-nuclei. On the other hand, the abundance of ^22^Ne left after s-processing has a large influence on the p-process via the ^22^Ne({alpha},n) reaction. We find that about 50% of p-nuclides are co-produced when normalized to their solar abundances in all adopted cases of seed distribution. Mo and Ru, which are largely underproduced in Type II supernovae (SNe II), are produced more than in SNe II although they are underproduced with respect to the yield levels of other p-nuclides. The ratios between p-nuclei and iron in the ejecta are larger than the solar ratios by a factor of 1.2. We also compare the yields of oxygen, iron, and p-nuclides in SNe Ia and SNe II and suggest that SNe Ia could make a larger contribution than SNe II to the solar system content of p-nuclei.