Johnson suffered the injury on the last play of Thursday's practice, coach Bruce Arians said. Johnson had ice taped to his upper right leg after Thursday's practice.
Arians said Johnson could miss one to two weeks.
"We will not know the extent of it," Arians said after Saturday night's game.
The Cardinals signed Johnson, a three-time Pro Bowler who played for the New York Jets last season, to a one-year deal on Monday. Before the injury, Johnson was expected to get five or six carries in Saturday's game.