Catalyzes the reversible isomerization of methylmalonyl-CoA (MMCoA) (generated from branched-chain amino acid metabolism and degradation of dietary odd chain fatty acids and cholesterol) to succinyl-CoA (3-carboxypropionyl-CoA), a key intermediate of the tricarboxylic acid cycle. {ECO:0000269|PubMed:1346616, ECO:0000269|PubMed:1978672, ECO:0000269|PubMed:21138732, ECO:0000269|PubMed:24458, ECO:0000269|PubMed:2453061, ECO:0000269|PubMed:25125334, ECO:0000269|PubMed:27167370, ECO:0000269|PubMed:28101778, ECO:0000269|PubMed:28943303, ECO:0000269|PubMed:29056341}. This is the function of MMUT (methylmalonyl-CoA mutase, ENSG00000146085).