Burnett struggled in his two appearances against the Cardinals last week, blowing two saves after allowing a combined three runs on five hits in 1 1/3 innings. Burnett also dealt with elbow tightness after the All-Star break, though he never landed on the disabled list.
"He has a little bit of irritation there, so I'm just staying off him," Johnson said. "With the expanded roster, you just give the guy some rest."
For the majority of the season, Burnett has been a solid eighth-inning pitcher for the Nats. In 50 2/3 innings this season, Burnett is 1-1 with two saves and a 2.49 ERA.
The Nationals' bullpen nevertheless received a boost on Monday, when Zach Duke and Christian Garcia were called up from Triple-A Syracuse. To make room on the 40-man roster, Henry Rodriguez (elbow) was transferred to the 60-day disabled list.