Aims: We present results from MUSE observations of the nearly face-on disk galaxy NGC 7742. This galaxy hosts a spectacular nuclear ring of enhanced star formation, which is unusual in that it is hosted by a non-barred galaxy, and because this star formation is most likely fuelled by externally accreted gas that counter-rotates with respect to its main stellar body. Methods: We used the MUSE data to derive the star-formation history (SFH) and accurately measure the stellar and ionized-gas kinematics of NGC 7742 in its nuclear, bulge, ring, and disk regions. Results: We have mapped the previously known gas counter-rotation well outside the ring region and deduce the presence of a slightly warped inner disk, which is inclined at approximately 6° compared to the outer disk. The gas-disk inclination is well constrained from the kinematics; the derived inclination 13.7° ± 0.4° agrees well with that derived from photometry and from what one expects using the inverse Tully-Fisher relation. We find a prolonged SFH in the ring with stellar populations as old as 2-3 Gyr and an indication that the star formation triggered by the minor merger event was delayed in the disk compared to the ring. There are two separate stellar components: an old population that counter-rotates with the gas, and a young one, concentrated to the ring, that co-rotates with the gas. We recover the kinematics of the old stars from a two-component fit, and show that combining the old and young stellar populations results in the erroneous average velocity of nearly zero found from a one-component fit. Conclusions: The spatial resolution and field of view of MUSE allow us to establish the kinematics and SFH of the nuclear ring in NGC 7742. We show further evidence that this ring has its origin in a minor merger event, possibly 2-3 Gyr ago. Data used for the flux and kinematic maps (Figs. 1 and 3-5) are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/612/A66