The 40-year-old Johnson will be making his third straight start in place of Tony Romo, who has been out with a broken finger on his throwing hand.
Brooks Bollinger will be Johnson's backup against the Giants Sunday.
Johnson has completed 36-of-67 passes for 356 yards with two touchdowns this season. He has been intercepted three times.
Senate Democrats to pull all-nighter on climate change
Susan Sarandon 'very excited' about daughter's pregnancy