Strasburg left Friday night's game against the Braves after two innings. Strasburg was examined in Washington on Saturday.
Johnson said the strain is "kind of up his back on the right side. Maybe it will go away. It's a little different than if it were lower and on the side more."
Johnson said there is no need to rush a decision on Strasburg's status for his next start on Thursday. The Nationals have an off day on Monday, and Johnson said Saturday Strasburg's next start could be pushed back if necessary.
"We'll see how he feels," Johnson said.
"If he's not having any discomfort and it's not grabbing him, he won't miss a start. But if it's bothering him he'll probably miss a start and see if it eases up for him and he doesn't have to do anything more than that."
Johnson said it was too early to look at how he might adjust the rotation to give Strasburg extra rest.
"It's premature to be doing that," Johnson said. "Let's see how he's feeling today and how he's feeling tomorrow. Then we'll take it from there."
Strasburg's start in the Nationals' 3-2 win Friday night was the shortest of his career. He grimaced after throwing a change-up to Brian McCann with one out in the second but completed the inning.
Craig Stammen relieved Strasburg to begin the third.
Another starting pitcher, Ross Detwiler, is on the 15-day disabled list with a back strain.
Strasburg is 3-5 with a 2.54 ERA in 12 games. He was 15-6 with a 3.16 ERA in 2012.
The Nationals on Saturday placed outfielder Bryce Harper on the 15-day disabled list with bursitis in his left knee. Right-hander Erik Davis was called up from Triple-A Syracuse to pitch out of the bullpen.
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