The Championship club confirmed on Monday that the Ivory Coast international has been diagnosed with Non-Hodgkin lymphoma.
A club statement read: "With the close support of the club's medical team, Sol has immediately started a course of chemotherapy treatment.
"Universally admired by teammates, staff and supporters in the Welsh capital, Sol has begun his battle in typically positive spirits and will continue to be an integral part of the Bluebirds family.
"During treatment, Sol will support his teammates at matches and our younger players within the academy, with whom he will continue his coaching development.
"All future updates on Sol's progress will be provided only via official Club channels. While we request privacy for him and his family at this time, messages of support to be passed on to Sol may be sent to email@example.com. We are all with you, Sol."
Bamba joined Cardiff in 2016 and helped them achieve promotion to the Premier League in 2018.
The 35-year-old has also made 46 international appearances and featured at the 2008 Olympics, 2014 World Cup and two Africa Cup of Nations tournaments.