Joeckel suffered a high fracture in his right ankle during the first quarter of his side's 34-20 defeat to the St Louis Rams yesterday, picking up the injury when his leg got caught underneath him under a mass of bodies at the end of a running play.
The Jaguars traded first-choice left tackle Eugene Monroe to the Baltimore Ravens last week, moving Joeckel over from right tackle having selected the rookie with the second overall pick in April's Draft.
"It wasn't pretty. That's tough. My heart goes out to him because he was playing well and he was eager to get in at left tackle," Jaguars quarterback Blaine Gabbert told reporters.
"That's the rough part about this game. It is a physical sport and injuries like that do happen."
The Jaguars' defeat leaves them still looking for their first win of the season ahead of this weekend's clash with the unbeaten Denver Broncos.