All players were required to get tested upon arriving at their camps on July 1 and they are expected to be tested every other day over the course of the season.
Those who test positive will be required to self-isolate until they test negative twice, allowing them to rejoin the team.
The Nationals will already be short-handed heading into the 2020 season with Ryan Zimmerman and Joe Ross opting out of competing.
"We are one-hundred percent supportive of their decision to not play this year," general manager Mike Rizzo said in a statement.
Washington will also be without Anthony Rendon, who signed a seven-year, $245 million contract with the Los Angeles Angels in free agency after finishing third in MVP voting last season.
The Nationals should still have plenty of talent on the roster after winning the first World Series in franchise history last season. According to Caesars, the squad has 18-1 odds to defend its championship with a title in 2020.