The league will mandate the use of surgical masks - not cloth ones - during travel and require each team to travel with a compliance officer, Passan reports.
Players on the road will be encouraged to not leave their hotel except for games.
The league is investigating whether players are following social-distancing guidelines and wearing masks, as well as rumors that Marlins players were going out at night in Atlanta during the preseason.
Miami has been unable to play since Sunday, and all of its games through this coming Sunday are postponed as a result of 18 total staff members - 16 players and two coaches - testing positive for COVID-19.
New York wound up scheduling a replacement series against the Baltimore Orioles at Camden Yards, which began Wednesday. The Orioles were supposed to be in Miami for the Marlins' home opener.