In this paper, we extend some results of D. Dolzan {on finite rings} to profinite rings, a complete classification of profinite commutative rings with a monothetic group of units is given. We also prove the metrizability of commutative profinite rings with monothetic group of units and without nonzero Boolean ideals. Using a property of Mersenne numbers, we construct a family of power $2^{\aleph _0}$ commutative non-isomorphic profinite semiprimitive rings with monothetic group of units.