Epistasis is an evolutionary phenomenon whereby the effect of a mutation depends on the genetic background in which it arises. A major source of epistasis in an RNA molecule is its secondary structure, which contains functionally important topological motifs held together by Watson-Crick (WC) base pairs. Here we study epistasis in the secondary structure of the novel RNA coronavirus SARS-CoV-2 by considering population-level frequencies of mutations at ancestral WC base paired sites across the genome. We uncover lower frequencies of mutations at WC than at non-WC base paired sites, supporting the hypothesis that modifications of the SARS-CoV-2 secondary structure are generally deleterious. Further, we find that mutations that convert WC base pairs to G:U “wobble” base pairs are approximately three times more frequent than those that abolish base pairing, suggesting that weak base pairing maintains some integrity of the SARS-CoV-2 secondary structure. Last, we show that WC base paired sites under the strongest epistatic constraint are primarily located in a pseudoknot motif that is involved in programmed ribosomal frameshifting, whereas those under the weakest epistatic constraint are located in a complex motif that is associated with viral pathogenicity. Together, these findings demonstrate the evolutionary importance of the SARS-CoV-2 secondary structure, as well as highlight specific topological motifs and associated viral functions that may be targets of different forms of natural selection.