Parsons, 70, will be replaced by Strauss Zelnick, who founded the media-focused private equity firm Zelnick Media Capital. Zelnick, currently chairman and CEO of Take-Two Interactive, also joined the CBS board in September.
"Unfortunately, unanticipated complications have created additional new challenges, and my doctors have advised that cutting back on my current commitments is essential to my overall recovery," Parsons said in a statement.
The CBS board shake-up took place early last month when then-CEO Leslie Moonves was ousted after allegations of sexual assault and harassment surfaced. Moonves has denied wrongdoing.
At the time of Moonves' exit, CBS also announced a deal to end litigation against controlling shareholder Shari Redstone and National Amusements for control of the broadcasting and media giant.
Six CBS board members stepped down, and new directors were appointed, including Parsons and Zelnick.
"I trust CBS' distinguished Board, now led by Strauss Zelnick, as well as CBS' strong management team led by [interim CEO] Joe Ianniello, will continue to successfully guide this Company into its very bright future," Parsons said.
Parsons was CEO of Time Warner from 2002 to 2007 and chairman of Time Warner's board from May 2003 to January 2009. He then served as chairman of Citigroup for three years.
— Reuters contributed to this report.