Alkaline-earth-like transition-metal atoms such as Zn and Cd are promising candidates for precision measurements and quantum many-body physics experiments. Here, we theoretically investigate the properties of diatomic molecules containing these closed-shell atoms. We calculate potential energy curves, permanent electric dipole moments, and spectroscopic constants for molecules consisting of either a Zn or Cd atom interacting with an alkali-metal (Li, Na, K, Rb, Cs, Fr) or alkaline-earth-metal (Be, Mg, Ca, Sr, Ba, Ra) atom. We use the ab initio electronic structure coupled cluster method with single, double, and triple excitations combined with large Gaussian basis sets and small-core relativistic energy-consistent pseudopotentials for heavier atoms. We predict that the studied molecules in the ground electronic state are chemically reactive weakly bound van der Waals complexes with small permanent electric dipole moments. The present results may be useful for spectroscopy and application of the studied molecules in modern ultracold physics and chemistry experiments.