We demonstrate that the high pressure of the hot intracluster medium (ICM) can trigger the collapse of molecular clouds in a spiral galaxy, leading to a burst of star formation in the clouds. Our hydrodynamical simulations show that the high gaseous (ram pressure and static thermal) pressure of the ICM strongly compresses a self-gravitating gas cloud within a short timescale (∼107 yr), dramatically increasing the central gas density and consequently causing efficient star formation within the cloud. The stars developed in the cloud form a compact, gravitationally bound star cluster. The star formation efficiency within such a cloud is found to depend on the temperature and the density of the ICM and the relative velocity of the galaxy with respect to it. Based on these results, we discuss the origin of starburst/post-starburst populations observed in distant clusters, the enhancement of star formation for galaxies in merging clusters, and the isolated compact H iiregions recently discovered in the Virgo Cluster.