"I'm in some pain," said Rodgers, adding that a timetable for his return remains undetermined.
Rodgers sustained the injury when Chicago Bears defensive end Shea McClellin sacked him from behind and Rodgers landed hard on his left, non-throwing shoulder only 2 1/2 minutes into the Bears' 27-20 win at Lambeau Field on Monday night.
Rodgers said he won't need surgery.
A potential option to replace him became available Tuesday. Former Packers quarterback Matt Flynn, cut Monday by the Buffalo Bills, cleared waivers and is now a free agent, according to ProFootballTalk.
Since leaving Green Bay as an unrestricted free agent, Flynn was traded by the Seattle Seahawks and released by the Oakland Raiders and Bills in the past 18 months.
In other Packers news, tight end Jermichael Finley went on injured reserve due to a spinal cord contusion. Green Bay also activated tackle Derek Sherrod from the physically unable to perform list and placed linebacker Sam Barrington on injured reserve.
--Quarterback Matt Flynn, cut Monday by the Buffalo Bills, cleared waivers Tuesday and is now a free agent, according to ProFootballTalk.
Speculation had the Green Bay Packers interested in bringing back Flynn after Aaron Rodgers fractured his collarbone Monday night and is expected to miss at least three weeks.
Since leaving Green Bay as an unrestricted free agent, Flynn has been traded by the Seattle Seahawks and released by the Oakland Raiders and Bills in the past 18 months.
The Packers were low in the priority, which meant another team could have claimed Flynn. The Packers made no claim either.
--Houston Texans head coach Gary Kubiak was released from a hospital Tuesday, but he is not expected to return to the team for at least one week.
Kubiak spent two nights in the hospital and a series of tests Monday determined he experienced a "mini-stroke" Sunday night.
Kubiak collapsed while jogging off the field toward the locker room at halftime during the Texans' game Sunday night against the Indianapolis Colts at Houston's Reliant Stadium.
Defensive coordinator Wade Phillips replaced Kubiak in the head coach role for the Texans and will operate in that capacity until further notice, the team confirmed.
--At the request of head coach Joe Philbin and owner Stephen Ross, the NFL opened its investigation into alleged misconduct by Jonathan Martin's teammates with the Miami Dolphins.
The NFL Players Association remains an interested observer in the investigation, the organization announced in a statement.
Martin, a second-year offensive tackle, turned over evidence to his family and representatives Sunday. The NFL also received and reviewed multiple text and voicemail messages from teammate Richie Incognito, NFL Network reported. Incognito was suspended indefinitely Sunday, not long after Philbin said he first learned of the misconduct allegations from Martin's agent.
Martin left the team last week after an incident, initially portrayed as a prank, in the team cafeteria led to an emotional breakdown.
--Chicago Bears quarterback Jay Cutler, who missed Monday's game against the Green Bay Packers due to a groin tear, aims to be available to face the Detroit Lions on Sunday, according to an ESPN report. The Bears would not confirm the report.
The team doesn't have a full practice scheduled until Thursday due to the Monday night game.
--Defensive end DeMarcus Ware is ready to return from a quadriceps injury, just in time for the Dallas Cowboys' game Sunday night at New Orleans.
Ware missed the past three games as opposing quarterbacks pile up record numbers against the Cowboys' lackluster defense. Quarterbacks are averaging 305.2 passing yards per game, completing 63.5 percent of their passes with 16 touchdowns.
The Cowboys also waived-injured defensive tackle Marvin Austin, who missed Sunday's game against the Minnesota Vikings with a back injury.
--Defensive tackle Kheeston Randall signed with the Cincinnati Bengals.