Jets general manager Mike Tannenbaum says the team has "made our disappointment clear to Braylon" and added that further punishment Edwards may face will be determined by the NFL.
Edwards was arraigned after a breath test showed he had a blood-alcohol level twice the legal limit when he was stopped, prosecutors said. Edwards apologized to the team, fans and his family on Wednesday. Jets owner Woody Johnson told Edwards that his behavior was unacceptable.
Through two games, Edwards has six catches for 54 yards and a touchdown.
As expected, center Nick Mangold (shoulder) and LB Jason Taylor (elbow) are active against the Dolphins. Sunday night's inactives include: QB Kellen Clemens (third quarterback), CB Darrelle Revis, RB Joe McKnight, LB Kenwin Cummings, T Wayne Hunter, TE Jeff Cumberland, DL Marcus Dixon, and LB Calvin Pace.
The Associated Press contributed to this report.