We have analyzed molybdenum isotopes, together with strontium and barium isotopes, in 18 presolar silicon carbide grains using the Chicago Instrument for Laser Ionization (CHILI), a resonance ionization mass spectrometer. All observed isotope ratios can be explained by mixtures of pure s-process matter with isotopically solar material. Grain residues were subsequently analyzed for carbon, nitrogen, silicon, and sulfur isotopes, as well as a subset for 26Al–26Mg systematics using the NanoSIMS. These analyses showed that all but one grain are mainstream grains, most probably coming from low-mass asymptotic giant branch (AGB) stars. One grain is of the AB type, for which the origin is still a matter of debate. The high precision of molybdenum isotope measurements with CHILI provides the best estimate to date for s-process molybdenum made in low-mass AGB stars. The average molybdenum isotopic abundances produced by the s-process found in the analyzed mainstream SiC grains are 0% 92Mo, 0.73% 94Mo, 13.30% 95Mo, 36.34% 96Mo, 9.78% 97Mo, 39.42% 98Mo, and 0.43% 100Mo. Solar molybdenum can be explained as a combination of 45.9% s-process, 30.6% r-process, and 23.5% p-process contributions. Furthermore, the observed variability in the individual grain data provides insights into the variability of conditions (neutron density, temperature, and timescale) during s-process nucleosynthesis in the grains' parent stars, as they have subtle effects on specific molybdenum isotope ratios. Finally, the results suggest that the ratio between p- and r-process molybdenum in presolar SiC from many different types of parent stars is Mop/Mor = 0.767, the value inferred for the solar system and consistent with what has been found in bulk samples and leachates of primitive meteorites.