The Galactic B[e] supergiant MWC 137 is surrounded by a large-scale optical nebula. To shed light on the physical conditions and kinematics of the nebula, we analyze the optical forbidden emission lines [N II] λλ 6548,6583 and [S II] λλ 6716,6731 in long-slit spectra taken with ALFOSC at the Nordic Optical Telescope. The radial velocities display a complex behavior but, in general, the northern nebular features are predominantly approaching while the southern ones are mostly receding. The electron density shows strong variations across the nebula with values spreading from about zero to ~800 cm-3. Higher densities are found closer to MWC 137 and in regions of intense emission, whereas in regions with high radial velocities the density decreases significantly. We also observe the entire nebula in the two [S II] lines with the scanning Fabry-Perot interferometer attached to the 6 m telescope of the Special Astrophysical Observatory. These data reveal a new bow-shaped feature at P.A. = 225°-245° and a distance 80″ from MWC 137. A new Hα image has been taken with the Danish 1.54 m telescope on La Silla. No expansion or changes in the nebular morphology appear within 18.1 yr. We derive a mass of ${37}_{-5}^{+9}\,{M}_{\odot }$ and an age of 4.7 ± 0.8 Myr for MWC 137. Furthermore, we detect a period of 1.93 d in the time series photometry collected with the TESS satellite, which could suggest stellar pulsations. Other, low-frequency variability is seen as well. Whether these signals are caused by internal gravity waves in the early-type star or by variability in the wind and circumstellar matter currently cannot be distinguished. * Based on observations collected with (1) the Nordic Optical Telescope, operated by the Nordic Optical Telescope Scientific Association at the Observatorio del Roque de los Muchachos, La Palma, Spain, of the Instituto de Astrofisica de Canarias, (2) the Danish 1.54 m telescope at La Silla, Chile, and (3) the 6 m telescope of the Special Astrophysical Observatory (SAO), Russia.