The 46-year-old has missed his side's last four matches, the latest a 3-1 defeat to Rotherham on Tuesday night, with assistant Shaun Taylor taking control in his absence.
"He (Ling) is receiving specialist care and, while we are able to report that he is making some progress, it is anticipated that Martin will be away from work for several weeks," a statement on Torquay's official website said.
"Any further statement will only be issued when it is appropriate to do so and, until then, the club would ask that the privacy of Martin's family be respected.
"The club and the League Managers Association are both fully supportive and are looking forward to his return."
After discussions with Taylor, the Gulls have begun searching for an experienced coach to assist the former Swindon centre-back with the running of the League Two side.