Not all stars exhibiting the optical spectral characteristics of B[e] stars share the same evolutionary stage. The Galactic B[e] star MWC 137 is a prime example of an object with uncertain classification, with previous work suggesting pre- and post-main sequence classification. Our goal is to settle this debate and provide reliable evolutionary classification. Integral field spectrograph observations with VLT MUSE of the cluster SH 2-266 are used to analyze the nature of MWC 137. A collimated outflow is discovered that is geometrically centered on MWC 137. The central position of MWC 137 in the cluster SH 2-266 within the larger nebula suggests strongly that it is a member of this cluster and that it is both at the origin of the nebula and the newly discovered jet. Comparison of the color-magnitude diagram of the brightest cluster stars with stellar evolutionary models results in a distance of about 5.2$pm$1.4 kpc. We estimate that the cluster is at least 3 Myr old. The jet extends over 66 (1.7 pc) projected on the plane of the sky, shows several knots, and projected velocities of up to $pm$450 km s$^{-1}$. From the Balmer emission line decrement of the diffuse intracluster nebulosity we determine E(B-V)=1.4 mag for the inner 1 cluster region. The spectral energy distribution of the brightest cluster stars yield a slightly lower extinction of E(B-V)~1.2 mag. The extinction towards MWC 137 is estimated to be E(B-V)~1.8 mag (A$_V$~5.6 mag). Our analysis of the optical and near-infrared color-magnitude and color-color diagrams suggests a post-main sequence stage of MWC 137. The existence of a jet in this object implies the presence of an accretion disk.
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