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We study the model of close-packed dimers on planar lattices belonging to the family of modified rectangular (MR) fractals, whose members are enumerated by an integer p ≥ 2 , as well as on the non-planar 4-simplex fractal lattice. By applying an exact recurrence enumeration method, we determine the asymptotic forms for numbers of dimer coverings, and numerically calculate entropies per dimer in the thermodynamic limit, for a sequence of MR lattices with 2 ≤ p ≤ 8 and for 4-simplex fractal. We find that the entropy per dimer on MR fractals is increasing function of the scaling parameter p , and for every considered p it is smaller than the entropy per dimer of the same model on 4-simplex lattice. Obtained results are discussed and compared with the results obtained previously on some translationally invariant and fractal lattices. • A close-packed dimer model has been studied on fractal lattices. • Exponential growth of the number of dimer configurations is established and entropies per dimer calculated. • Nontrivial role of all lattice parameters is observed. • Inefficiency of recursive enumeration on the whole family of fractals is related to partitions. [ABSTRACT FROM AUTHOR]