Grimes tore his Achilles tendon in Atlanta's 40-24 season-opening victory over Kansas City on Sunday.
Second-year cornerback Johnson, who played 10 games with two starts for the Indianapolis Colts in 2011, has been added to a secondary where back-ups Chris Owens and Dominique Franks will now be expected to take plenty of snaps.
The Falcons host Peyton Manning and the Denver Broncos on Monday and Owens said he was looking forward to the challenge of competing for the open position.
"I'm excited about the opportunity, and it's all about being focused. We've got a great challenge with Peyton ahead of us, so it's gonna be a good one," said Owens.
Robinson will stay on the right for the Falcons while four-time Pro Bowl selection Samuel will take over in Grimes' position on the left side.