Context : Blue compact galaxies ( BCG ) are gas-rich , low-mass , small systems that form stars at unusually high rates . This makes them excellent laboratories for investigating the process of star-formation ( SF ) at galactic scales and the effects of massive stellar feedback on the interstellar ( and intergalactic ) medium . Aims : We analyzed the BCG Tololo 1937-423 using optical integral field spectroscopy to probe its morphology , stellar content , nebular excitation and ionization properties , and the kinematics of its warm ionized gas . Methods : Tololo 1937-423 was observed with the Visible Multi-Object Spectrograph at the Very Large Telescope . We took data in the wavelength range 4150-7400 Å , covering a field of view of 27 \arcsec \times 27 \arcsec on the sky with a spatial sampling of 0 \aas@@fstack { \prime \prime } 67 . From these data we built maps in the continuum and brighter emission lines , diagnostic line ratio maps , and velocity dispersion fields . We also generated the integrated spectrum of the main H ii regions and young stellar clusters to determine reliable physical parameters and oxygen abundances . Results : We found that Tololo 1937-423 is currently undergoing an extended starburst . In the H \alpha maps we identified nine major clumps , aligned mostly northeast-southwest , and stretching to galactocentric distances \geq 2 kpc . The galaxy presents a single continuum peak that is not cospatial with any knot in emission lines , indicating at least two relatively recent episodes of SF . The inhomogeneous dust distribution reachs its maximum [ E ( B-V ) \sim 0.97 ] roughly at the position of the continuum peak . We found shocked regions in the galaxy outer regions and at the edges of the SF knots . The oxygen abundance , 12+log ( O/H ) \sim 8.20 \pm 0.1 , is similar in all the SF regions , suggesting a chemically homogeneous ionized interstellar medium over spatial scales of several kpc . The ionized gas kinematics displays an overall regular rotation around a northwest-southeast axis , with a maximum velocity of 70 \pm 7 km s ^ { -1 } . Conclusions : The morphology of the galaxy and the two different episodes of SF suggest a scenario of triggered ( induced by supernova shock waves ) SF acting in Tololo 1937-423 . The inferred ages for the different SF episodes ( \sim 13-80 Myr for the central post-starburst and 5-7 Myr for the ongoing SF ) are consistent with triggered SF , with the most recent SF episode caused by the collective effect of stellar winds and supernova explosions from the central post-starburst . The velocity dispersion pattern , with higher velocity dispersions found at the edges of the SF regions , and shocked regions in the galaxy , also favor this scenario .