Suppress COVID-19 Act of 2020 This bill provides additional funding for states, tribes, and territories to procure tests and related supplies and undertake contact tracing and other public health measures to suppress COVID-19 (i.e., coronavirus disease 2019) and the virus that causes it. It also reallocates certain other funding to jurisdictions for such public health measures. The additional amounts provided by the bill are designated as an emergency requirement pursuant to the Statutory Pay-As-You-Go Act of 2010 (PAYGO) and the Senate PAYGO rule, which excludes the budget effects from being counted for purposes of enforcing the PAYGO rules. In particular, the bill authorizes the formation of interstate compacts of states, tribes, and territories to procure COVID-19 tests and supplies, and it specifically reserves a portion of funding for jurisdictions that join compacts that meet requirements for transparency, governance, anti-corruption, and timeliness of test results. The Department of Health and Human Services (HHS) must also support the formation of, and cooperate with, these compacts. The bill also provides additional funding, and reallocates existing funding, specifically for contact tracing and other public health measures. To receive such funding, a jurisdiction must submit a plan, developed with relevant stakeholders, to HHS that details how it will suppress COVID-19 to levels recommended by the Centers for Disease Control and Prevention. HHS must provide guidance and undertake other efforts to coordinate these plans, such as by developing shared indicators. HHS must report within 30 days to Congress concerning the timeline for the distribution of these funds.