Manager Matt Williams said Scherzer may be ready to start within a few days.
"I would think that before another five days he'd be OK to go," Williams said before an 8-4 loss to the Atlanta Braves on Monday night. "We have to get him on a [mound] and make sure he can throw all his pitches. So that may happen tomorrow."
Williams said Scherzer had difficulty throwing his slider due to the thumb, which the pitcher jammed while batting against St. Louis Cardinals on Thursday. Scherzer could not throw in the bullpen session Sunday.
Following his injury batting and the reported season-ending Achilles injury to the Cardinals' Adam Wainwright, Scherzer told CBS Sports that it's time for the designated hitter to be used in both leagues.
"If you look at it from the macro side, who'd people rather see hit: Big Papi [Boston Red Sox slugger David Ortiz] or me?" Scherzer told the website. "Who would people rather see, a real hitter hitting home runs or a pitcher swinging a wet newspaper? Both leagues need to be on the same set of rules."
In the first year of a $210 million, seven-year contract, Scherzer is 1-2 with a 1.26 ERA in four starts.
Williams said he did not intend to announce a replacement starter until after Monday night's game against the Braves. He said right-hander Tanner Roark, who has made six relief appearances, could start but might last only 50 to 60 pitches.
Roark was 15-10 with a 2.85 ERA in 31 starts last year.
"Tanner's fully loaded if we want to go that way," Williams said.
Right-hander A.J. Cole could be recalled from Triple-A Syracuse after being held out of scheduled start Monday.
"That's an 'in case,'" Williams said.
Third baseman Anthony Rendon was scratched from a scheduled injury rehabilitation game with Double-A Harrisburg on Monday due to fatigue. Recovering from a left knee sprain, Rendon was 2-for-4 with a double in his first two games.
Williams said Rendon is working at third base and second base at Harrisburg in preparation to play both positions with the Nationals.
Information from The Associated Press was used in this report.