"Just get better now," Morse said. "We asked for anything we can do, and they said the best thing is to just let it calm down."
Morse and manager Davey Johnson said the outfielder would sit out Wednesday's series finale -- Roger Bernadina batted sixth and played left field -- and rest on Thursday's off-day before re-evaluating on Friday in Atlanta.
"His left hand is his dominant hand when he's hitting," Johnson said. "It's been bothering him about a month and he's been trying to play through it."
Morse injured his right hand when jammed during an at-bat in San Francisco in August and when he favored that hand, he said he overcompensated with his left and injured the left wrist.
"He got hit on his right hand, but his left hand is his dominant hand and he drags the bat through with it with a lot of force, that's why he's got tremendous power," Johnson said. "Obviously it's been bothering him. His bat's been slow. He's had to cheat to get through it."
Johnson said the sheath was inflamed and Morse would receive some anti-inflammatory medication. The Nationals planned to send the test on to Baltimore for a specialist to examine.
Morse, batting .285 with 13 homers and 49 RBIs this season, has been slowed by injuries all season and has appeared in just 88 games.
"It's been a tough year. Tough year," Morse said. "I try to help the team as much as possible."