Braun, who left in the eighth inning of Sunday's game, did not want the MRI exam and wants to play on Tuesday against Puerto Rico.
"I want to play tomorrow," Braun said. "That's my intent."
Johnson said that the Brewers said the player has a tendency to not admit when he's hurt.
"He wanted me to keep an open mind and let him swing tomorrow," Johnson said. "I know ballplayers. ... I [said], 'I know you're lying to me right now. I also got word from the Brewers you might not be honest with me.'"
Brewers management decided to let Braun stay in Miami with Team USA.
"They work out today. He won't work out and probably will not play tomorrow just as a precaution. This is one of these literal day-to-day [injuries]," Brewers assistant general manager Gord Ash said. "We'll reconnect tomorrow, see how he is and see if we need to do anything. He's not going to come here or go to Milwaukee for any examination at this point."
Braun, who was checked out by the Marlins' medical staff, spoke with Brewers trainer Roger Caplinger, who agreed that the injury sounded minor.
"You're guided by the physician [there] and we're comfortable with that. And more importantly, comfortable with what the player tells us," Ash said.
The injury is on the same side that Braun hurt during a swing in a game on Aug. 9. Braun took six games off, but Ash said this intercostal strain is lower in his rib cage.
"Similar, but much milder," Ash said.
The 25-year-old Braun hit .300 with 30 homers in 114 games before last year's injury, and .238 with seven home runs in the final 37 games. He had only eight extra-base hits in September.
Brewers manager Ken Macha said he wasn't overly concerned since there's still three weeks left in spring training.
"Injuries happen," Macha said. "It's the weather and your wife, you have no control over those two or injuries."