Positive-strand RNA virus genomes are translated into polyproteins that are processed by viral proteases to yield functional intermediate and mature proteins. Coronaviruses (CoVs) carry genes that encode an nsp5 protease (also known as 3CLpro or Mpro) responsible for 11 maturation cleavages. The nsp5 structure contains two chymotrypsin-like domains (D1 and D2) and a unique domain (D3), and forms functional dimers. However, little is known of interactions or communication across the structure of the protease during nsp5 activity. Using reverse genetic mutagenesis of the CoV murine hepatitis virus (MHV) nsp5, we identified a new temperature-sensitive (ts) mutation in D2 of nsp5 (Ser133Ala) and confirmed a ts residue in D3 (Phe219Leu). Both D2-tsS133A and D3-tsF219L were impaired for viral replication and nsp5-mediated polyprotein processing at the nonpermissive temperature. Passage of tsS133A and tsF219L at the nonpermissive temperature resulted in emergence of multiple second-site suppressor mutations, singly and in combinations. Among the second-site mutations, a D2 His134Tyr change suppressed the ts phenotype of D2-tsS133A and D3-tsF219L, as well as the previously reported D2-tsV148A. Analysis of multiple CoV nsp5 structures, and alignment of nonredundant nsp5 primary sequences, demonstrated that ts and suppressor residues are not conserved across CoVs and are physically distant (>10 Å) from each other, from catalytic and substrate-binding residues, and from the nsp5 dimer interface. These findings demonstrate that long-distance communication pathways between multiple residues and domains of nsp5 play a significant role in nsp5 activity and viral replication, suggesting possible novel targets for non-active site inhibitors of nsp5.