Godwin was placed in concussion protocol Wednesday and underwent extra tests Saturday after participating in non-contact practice Friday. He was listed as doubtful on Tampa Bay's latest injury report.
The star wideout notched a team-high six receptions for 79 yards during the Buccaneers' 34-23 loss to the New Orleans Saints in Week 1.
He enjoyed his best NFL campaign last season, racking up 86 receptions for 1,333 yards and nine touchdowns through 14 games.
The 2019 Pro Bowler missed the first two games of his career last season due to a hamstring injury.
Tampa Bay drafted Godwin out of Penn State in the third round in 2017.