Farrell, who managed the Red Sox since 2013, will not return for the 2018 season, president of baseball operations Dave Dombrowski announced. The team said a search for a new manager will begin immediately.
"I thought it was the appropriate time to make a change for the betterment of the organization moving forward," Dombrowski said at a news conference. "You weigh a lot of different things to come into play. You watch day in, day out over a season. You come up with a decision based upon that. And for me, at this point, sometimes change can be better. That's why we've decided to move forward with the change."
Farrell, 55, was 432-378 (.533) in five seasons, leading the Red Sox to the World Series title in 2013. He was under contract through the end of the 2018 season.
Nationals manager Dusty Baker said Tuesday night that Strasburg was too ill to start Wednesday's game before the dramatic reversal by the team.
The Nationals made the move official a few hours before 3:08 p.m. CT starting time.
Nationals general manager Mike Rizzo told reporters Wednesday that Strasburg started to feel flu-like symptoms after starting Game 1, which continued the next couple of days. Rizzo said Strasburg experienced fever, chills and continued to feel poorly when he threw his bullpen session on Monday.
Encarnacion has been sidelined for the last two contests with a sprained ankle that was sustained in the first inning of Game 2. The 34-year-old Dominican was injured when he jammed his foot into second base while trying to get back to the bag in time to avoid a double play.
Encarnacion batted .258 with 38 homers and 107 RBIs in his first season of a three-year contract. It marked his third straight season with at least 30 homers and 100 RBIs.