He rejoined the team Sunday, taking batting practice and fielding grounders.
Manager Dave Martinez said Murphy will accompany the team to New York, where it opens a two-game series against the Yankees on Tuesday. The Nationals will play five straight games in American League parks, where they'll need a designated hitter.
"I wanted to see where he's at and get him here, and he looked pretty good," Martinez said. "He played two days in a row (Double-A Harrisburg) so we didn't want him to do much, but we wanted to get him back here. So, we'll see how he feels tomorrow and we'll touch base and see where we go from there."
Murphy has finished second in batting in the National League each of his two seasons with the Nationals, hitting .347 in 2016 and .322 in 2017.
The Nationals had announced Saturday that Strasburg (right shoulder inflammation) was headed for the disabled list following an MRI. He left Friday night's start against the Giants after two innings.
Strasburg is 5-5 with a 3.46 ERA in 13 starts. He ranks fourth in the National League with 95 strikeouts. Kintzler is 1-2 with two saves, 13 holds and a 4.45 ERA in 31 appearances.
Setup man Kintzler (right forearm flexor strain) left Saturday's game against the Giants in the eighth inning with forearm tightness.
"I don't think it's anything serious," Kintzler said Sunday. "Probably just some rest and some strengthening. I don't know what the timetable is, but I'm sure it would be no more than 10 days whatever we need."
The team recalled right-hander pitchers Trevor Gott and Wander Suero from Triple-A Syracuse.
Gott returns to the Nationals for his third stint of the season. He has appeared in 17 games out of Washington's bullpen, going 0-2 with a 5.28 ERA.
Suero has appeared in 12 games for the Nationals, with a 4.15 ERA.
The Associated Press contributed to this report.