Peterson played 35 snaps last season on offense, catching six passes for 54 yards and running four times for 21 yards and completing a 17-yard pass.
"My duties are now done," Peterson said, via the team's website. "I'm completely OK with it."
Arians added that Peterson’s punt-returning duties will also be limited.
Peterson returned four punts for touchdowns during his rookie season in 2011. He only returned 33 punts last season.
"I think it's just going to take my game to another level now because, now, I don't have to focus on the punt returns. I don't have to focus on trying to remember the offensive plays," Peterson said. "Now, I can hone in on playing defensive back and just being the best player I can be."
Peterson had 42 total tackles, with three interceptions last season, earning first-team All Pro honors.