"He's got a crack in the ankle," coach Jack Del Rio said after his team's 24-17 victory. "The best-case scenario is about a month out, depending on how quickly he heals, and it could be worse. We just won't know until we see how the injury heals."
A source told ESPN's Chris Mortensen that doctors have told team officials Leftwich will probably miss closer to six weeks than four.
The injury occurred on the Jags' first offensive play. Leftwich stayed in the game for four more plays but later was carted off the field for X-rays. Shortly before halftime, the team announced he was done for the day with a sprained ankle.
The news that it was broken didn't come until Del Rio's postgame interview.
Leftwich was replaced by David Garrard, who capped the opening drive with a 16-yard touchdown run.
Leftwich was hurt when he was sacked by Arizona's Adrian Wilson and several others, a play that was nullified by a penalty against the Cardinals.
The third-year quarterback from Marshall has started 37 games for Jacksonville, including all 10 this season. He took over as starter four games into his rookie season after the Jaguars made him the seventh overall pick in the 2003 draft.
Jacksonville was already missing running back Fred Taylor with an ankle injury.
Information from The Associated Press was used in this report.