Byrd, 37, has a slash of .237/.286/.448 with 19 home runs and 42 RBIs in 388 plate appearances. Byrd will most likely place right fielder Hunter Pence, who went on the disabled list earlier this week.
The 24-year-old Johnson is a solid right hander pitcher with poor command. The 2012 sixth round pick has posted a 3.41 ERA in 58 innings at the Double-A level this season.
Byrd is an impending free agent and will most likely not sign back with the team, so the Giants gave up a younger pitcher for six weeks of Byrd.