Lanning stepped away following Australia's Commonwealth Games gold-medal success in Birmingham and it remains unclear when, or if, she will return.
"The club respects her decision and asks that her privacy continue to be respected," a Stars statement said.
Stars will need to find a new captain for their WBBL campaign which starts on October 15 against Brisbane Heat. Earlier this year Lanning had handed over the captaincy of Victoria to Sophie Molineux.
With Lanning now ruled out of the WBBL it also increases the prospects of Australia needing a new captain for their tour of India in mid-December.
When Shelley Nitschke was confirmed as the new permanent head coach last week she said that conversations about Lanning's future had not yet taken place.
"When the time is right we'll have those conversations about whether she is back in December or whenever it might be," she said.
"There are a good group of emerging leaders in our team that are going to have opportunities to stick their hands up," Nitschke said. "We don't have a designated leadership group but there are people amongst the team and group that are leaders on and off the field. Some girls lead in their states. They all have different strengths."
Lanning was named Australian captain when she was 21 and over the last few years has led the team to unprecedented success with the T20 and ODI World Cup titles, Commonwealth Games gold and multiple Ashes victories. She has also maintained her form as one of the leading batters in the world, averaging 53.53 in ODIs and 36.48 in T20Is.