Epistasis is an evolutionary phenomenon whereby the fitness effect of a mutation depends on the genetic background in which it arises. A key source of epistasis in an RNA molecule is its secondary structure, which contains functionally important topological motifs held together by hydrogen bonds between Watson–Crick (WC) base pairs. Here we study epistasis in the secondary structure of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) by examining properties of derived alleles arising from substitution mutations at ancestral WC base-paired and unpaired (UP) sites in 15 conserved topological motifs across the genome. We uncover fewer derived alleles and lower derived allele frequencies at WC than at UP sites, supporting the hypothesis that modifications to the secondary structure are often deleterious. At WC sites, we also find lower derived allele frequencies for mutations that abolish base pairing than for those that yield G·U “wobbles,” illustrating that weak base pairing can partially preserve the integrity of the secondary structure. Last, we show that WC sites under the strongest epistatic constraint reside in a three-stemmed pseudoknot motif that plays an essential role in programmed ribosomal frameshifting, whereas those under the weakest epistatic constraint are located in 3’ UTR motifs that regulate viral replication and pathogenicity. Our findings demonstrate the importance of epistasis in the evolution of the SARS-CoV-2 secondary structure, as well as highlight putative structural and functional targets of different forms of natural selection.