Shocks may have been prevalent in the early Universe, associated with virialization and supernova explosions, etc. Here, we study thermal evolution and fragmentation of shock-compressed clouds, by using a one-zone model with detailed thermal and chemical processes. We explore a large range of initial density (1-10 5 cm −3 ), metallicity (0-10 −2 Z ⊙ ), UV strength (0-500 times Galactic value), and cosmic microwave background temperature (10 and 30 K). Shock-compressed clouds contract isobarically via atomic and molecular line cooling, until self-gravitating clumps are formed by fragmentation. If the metals are only in the gas-phase, the clump mass is higher than ∼ 3 M ⊙ in any conditions we studied. Although in some cases with a metallicity higher than ∼ 10 −3 Z ⊙ , re-fragmentation of a clump is caused by metal-line cooling, this fragment mass is higher than ∼ 30 M ⊙ . On the other hand, if about half the mass of metals is condensed in dust grains, as in the Galactic interstellar medium, dust cooling triggers re-fragmentation of a clump into sub-solar mass pieces, for metallicities higher than ∼ 10 −5 Z ⊙ . Therefore, the presence of dust is essential in low-mass ( M ⊙ ) star formation from a shock-compressed cloud.