Specifically hydrolyzes 7-methylguanosine monophosphate (m(7)GMP) to 7-methylguanosine and inorganic phosphate (PubMed:23223233, PubMed:24603684). Also able to mediate hydrolysis of diphosphate (m(7)GDP) to 7-methylguanosine and 2 inorganic phosphate with lower activity (PubMed:23223233). The specific activity for m(7)GMP may protect cells against undesired salvage of m(7)GMP and its incorporation into nucleic acids (PubMed:23223233). Also has weak activity for CMP (PubMed:23223233, PubMed:24603684). UMP and purine nucleotides are poor substrates (PubMed:23223233, PubMed:24603684). H2O + N(7)-methyl-GMP = N(7)-methylguanosine + phosphate CMP + H2O = cytidine + phosphate a ribonucleoside 5'-phosphate + H2O = a ribonucleoside + phosphate Inhibited by high levels of AMP. kcat is 6.3 sec(-1) with m(7)GMP. kcat is 12 sec(-1) with CMP. kcat is 0.88 sec(-1) with GMP. kcat is 0.28 sec(-1) with AMP. kcat is 2.3 sec(-1) with UMP. Optimum pH is 7.5. Monomer. Belongs to the pyrimidine 5'-nucleotidase family.