Coach Doug Marrone said he doesn't yet know the full extent of Hurns' injury and was waiting on a report from the doctors to determine an early timetable for his return.
"I don't anticipate [Hurns playing] this week," Marrone said. "I would say yes for [missing this week], but I wouldn't know after that."
Hurns, who is second on the team in receptions (36) and receiving yards (446) and tied for first with two touchdown catches, was injured with less than a minute remaining in regulation in the Jaguars' 20-17 overtime victory over the Los Angeles Chargers on Sunday. He caught seven passes for 70 yards and was hurt on his final catch.
He was down for a moment before crawling to the sideline so the Jaguars would not incur a 10-second runoff because they were out of timeouts.
The Jaguars (6-3) also don't yet know the status of receiver Arrelious Benn, who suffered a knee injury against the Chargers. With Hurns and Benn potentially out for Sunday's game at Cleveland, the Jaguars have only three healthy receivers on the active roster.
Marqise Lee, the Jaguars' leading receiver this season (38 catches for 493 yards), has 153 career receptions. The other three have 43 combined: Jaelen Strong (28), Keelan Cole (14), and Jaydon Mickens (one). Strong hasn't been active on game day since the Jaguars claimed him off waivers from Houston on Sept. 19.
The Jaguars lost No. 1 receiver Allen Robinson to a torn left ACL in the season opener.