Aims. We derive the stellar mass function (SMF) of quiescent and star-forming galaxies at z ≤ 0.2 using 12-band (five broad plus seven narrow) photometry from the Javalambre Photometric Local Universe Survey (J-PLUS) third data release (DR3) over 3284 deg2, where the narrow bands improve photometric-redshift and stellar property precision relative to purely broadband surveys. Methods. We selected ∼890 000 galaxies with r ≤ 20 mag and photometric redshifts in the range 0.05 ≤ z ≤ 0.20 over an effective area of 2 881 deg2, corresponding to a comoving volume of V ≃ 1.6 × 108 Mpc3. Stellar masses and star formation rates were derived through spectral energy distribution (SED) fitting with the Code Investigating GALaxy Emission (CIGALE), and confronted with spectroscopic samples. Galaxies were classified as star-forming or quiescent based on their specific star formation rate (sSFR), adopting a threshold of log (sSFR [yr−1]) = −10.2. We computed SMFs for both populations using the 1/Vmax method, applied completeness corrections, and fit a parametric single Schechter function. Results. The SMFs derived from J-PLUS DR3 are well described by Schechter functions and agree with previous photometric and spectroscopic studies. The characteristic mass for quiescent galaxies, log (M★/M⊙) = 10.80, is higher by 0.4 dex than that of star-forming galaxies. The faint-end slope is steeper for star-forming galaxies (α = −1.2) than for quiescent ones (α = −0.7). The quiescent fraction increases by 40% per dex in stellar mass, reaching fQ > 0.95 at log (M★/M⊙) > 11. Comparisons with the GAlaxy Evolution and Assembly (GAEA) semi-analytic model show an overabundance of simulated star-forming galaxies, particularly at intermediate masses. Conclusions. The SMFs and quiescent fraction from J-PLUS DR3 are consistent with the literature and provide valuable constraints for galaxy formation models. Quiescent galaxies represent 45% of the number density at log M★ > 9 but contribute 75% of the stellar mass density. This work lays the groundwork for studies of environmental quenching using J-PLUS. The inclusion of seven narrowband filters improves redshift precision by 20%, enabling more accurate SED fitting and galaxy classification. These methods and findings can be extended with J-PAS, which will provide deeper and higher-resolution photometry over a wider spectral range.