Franklin, who rushed for 107 yards in 19 carries last season, was injured returning a kickoff against the Minnesota Vikings on Nov. 24.
The 5-foot-10, 205-pound rusher tweeted about the situation Thursday.
"Unfortunately this week I have been ruled out of returning for the 2014/15 season and returning to play in the NFL," Franklin said via Twitter. "But I understand God knows what he is doing for now he has another platform for me to step upon."
Coach Mike McCarthy told the Green Bay Press Gazette that more details on Franklin's situation would be announced Friday.
"I have some unfortunate news about Johnathan Franklin," McCarthy said. "The organization will address this tomorrow. All the information has come in. He will not be back with us. I can't say enough about him as a person. I don't know. He's as classy as anyone who's walked through these doors. His situation will be addressed tomorrow."
Franklin was selected in the fourth round of the NFL draft in 2013 after rushing for a school-record 4,369 yards at UCLA. He rushed for 31 touchdowns and scored three times on pass receptions for the Bruins.