Parrish suffered a back sprain in Sunday's 33-27 loss to the Bengals, Brianna Dix of the Buccaneers' official site reports.
Both the MRI and X-ray came back negative, so the cornerback has avoided any significant damage to his spine. Parrish's ability to return to the field will now be entirely dictated by how well he can manage and play through the pain. The 22-year-old's availability for Sunday's Week 2 game against the Browns will likely be determined by his level of participation during practice this week.