Red Sox chief baseball officer Chaim Bloom provided the news to reporters and noted the team is optimistic that Rodriguez, 27, would recover fully.
"This is not something you want to mess around with," Bloom said.
Rodriguez was one of the American League's best starting pitchers last season, going 19-6 with a 3.81 ERA and 213 strikeouts in 203.1 innings. He finished sixth in the AL Cy Young voting.
The southpaw tested positive for COVID-19 in March, per Matt Weyrich of NBC Sports Washington.
Per the Associated Press, Rodriguez was cleared for baseball activity and began participating July 18.
However, an MRI revealed the myocarditis, leading to his being shut down for a week.
"That's why the doctors tell me to just take a week, just rest, don't let your heart get too much heart rate," Rodriguez told reporters. "If it goes away, just go back to work."
But that time away has since turned into the entire season, as the team's medical staff felt his condition was serious enough to merit his continued absence.
Rodriguez also discussed his emotions after hearing the myocarditis diagnosis:
"That's the most important part of your body, so when you hear that, the first time I hear it was kind of scared a little. Now that I know what it is it's still scary, but I know exactly what it is. Just talk to my mom, talk to my wife, they know what I have and everything. Now we just gotta take the rest. That's hard, but you gotta take a rest."
Rodriguez's COVID-19 case was severe enough for him to tell reporters that he felt like he was "100 years old."
The Boston Globe's Pete Abraham gave an outlook for next year: "The expectations are ... Rodriguez will fully recover and pitch next season. His heart is functioning normally. He will return to Florida and return to Boston as needed for checkups."
Abraham also added the following: "Kudos to @eduardorod5 for allowing the Red Sox to discuss his non-baseball-related health situation with the media (which informs fans). Eddie's a good guy with a wife and two kids. Here's wishing him a full recovery."
Rodriguez has pitched five big league seasons, winning the 2018 World Series with the Sox.