Mr. Martinez also told reporters he believed that one of the dozen cases was a person who is unvaccinated, according to ESPN.
The Nationals are among many M.L.B. teams that have been able to loosen safety protocols after reaching the 85 percent vaccination threshold set by the league. Players and coaches on these teams do not have to wear masks in the dugout or bullpen during games, can work out without masks in weight rooms and are subject to less frequent testing for the virus.
The Nationals had a previous outbreak at the beginning of the season when their series against the Mets was postponed in April after four Nationals players and a staff member tested positive for the virus.
And after several Yankees players tested positive for the virus, that team had to postpone its July 15 game against the Red Sox.
The Nationals and Phillies are set to make up the Wednesday game as part of a doubleheader on Thursday.