During pilot observations of the Virgo Environmental Survey Tracing Galaxy Evolution (VESTIGE), a blind narrow-band H alpha + [NII] imaging survey of the Virgo cluster carried out with MegaCam at the CFHT, we have observed the spiral galaxy NGC 4254 (M99). Deep H alpha + [NIT] narrow-band and GALEX UV images reveal the presence of 60 compact (70-500 pc radius) star-forming regions up to similar or equal to 20 kpc outside the optical disc of the galaxy. These regions are located along a tail of HI gas stripped from the disc of the galaxy after a rapid gravitational encounter with another Virgo cluster member that simulations indicate occurred 280-750 Myr ago. We have combined the VESTIGE data with multifrequency data from the UV to the far-infrared to characterise the stellar populations of these regions and study the star formation process in an extreme environment such as the tails of stripped gas embedded in the hot intracluster medium. The colour, spectral energy distribution (SED), and linear size consistently indicate that these regions are coeval and have been formed after a single burst of star formation that occurred less than or similar to 100 Myr ago. These regions might become free floating objects within the cluster potential well, and be the local analogues of compact sources produced after the interaction of gas-rich systems that occurred during the early formation of clusters.