We study propagation effects due to the finite speed of light in ionization of extended molecular systems. We present a general quantitative theory of these effects and show under which conditions such effects should appear. The finite speed of light propagation effects are encoded in the non-dipole terms of the time-dependent Shrödinger equation and display themselves in the photoelectron momentum distribution projected on the molecular axis. Our numerical modeling for the H + 2 molecular ion and the Ne 2 dimer shows that the finite light propagation time from one atomic center to another can be accurately determined in a table top laser experiment which is much more readily affordable than the ground breaking synchrotron measurement by Grundmann et al [Science 370, 339 (2020)].