Godwin, who was selected to his first Pro Bowl this season, was ruled out against the Texans because of a hamstring injury, according to the team.
Arians said Godwin is "slowly" progressing in his rehab. When asked if he believes the wideout can return for the team's final regular-season game, he said, "I would hope so."
During last week's win over the Detroit Lions, Godwin notched five receptions for 121 receiving yards before suffering the hamstring injury in the third quarter. The team later ruled him out for the remainder of the contest.
Godwin ranks second in the NFL in receiving yards (1,333), trailing only New Orleans Saints wideout Michael Thomas. His nine receiving touchdowns are tied with Lions receiver Marvin Jones Jr. for second most.
The Buccaneers are already without three-time Pro Bowl receiver Mike Evans. He was placed on season-ending injured reserve this week with a hamstring injury.
The Texans can clinch the AFC South title with a win over the Buccaneers on Saturday.