The singer/guitar player took over from Buckingham after he quit ahead of the group's "Shake the Cage" Tour, in support of their 1987 album, "Tango in the Night". He went on to perform with the group through 1995 and appeared on the "Behind the Mask" and "Time" albums.
Taking to Facebook, the star's son, Billy Burnette, Jr., confirmed his dad had been hospitalised at the Vanderbilt University Medical Center in Nashville, Tennessee.
"Billy Burnette tested positive for Covid / Corona virus but he's tough and could be released from vanderbilt soon," he penned. "Everyone send up a prayer and send and post some of your favorite songs by him !! Thanks BbJr."
Despite appearing in the group for eight years, the star was not asked to return following Buckingham's recent 2018 departure. Before the announcement that Neil Finn and Mike Campbell had joined the group was made official, he took to Twitter to air his grievances.
"Breaking news: Lindsey Buckingham is out but I'm not in. A little p**sed off but I'll get over it," he wrote at the time, before swiftly deleting the post.