SARS-CoV-2 has emerged as a major threat to global public health, resulting in global societal and economic disruptions. Here, we investigate the intra- and intermolecular RNA interactions of wildtype (WT) and a mutant (Δ382) SARS-CoV-2 virus in cells using high throughput structure probing on Illumina and Nanopore platforms. We identified 12 potentially functional structural elements within the SARS-CoV-2 genome, observed that identical sequences can fold into divergent structures on different subgenomic RNAs, and that WT and Δ382 virus genomes can fold differently. Proximity ligation sequencing experiments identified hundreds of intra- and intermolecular pair-wise interactions within the virus genome and between virus and host RNAs. SARS-CoV-2 binds strongly to mitochondrial and small nucleolar RNAs and is extensively 2’-O-methylated. 2’-O-methylation sites in the virus genome are enriched in the untranslated regions and are associated with increased pair-wise interactions. SARS-CoV-2 infection results in a global decrease of 2’-O-methylation sites on host mRNAs, suggesting that binding to snoRNAs could be a pro-viral mechanism to sequester methylation machinery from host RNAs towards the virus genome. Collectively, these studies deepen our understanding of the molecular basis of SARS-CoV-2 pathogenicity, cellular factors important during infection and provide a platform for targeted therapy.