In a statement, the Birmingham-based band said he was "already up and about" and asked fans for privacy during his recuperation.
The band said they hoped he would make "a strong and speedy recovery" and that they would be back touring next year.
Campbell, a former professional spoon player, became lead singer of UB40 when his brother Ali left the group in 2008.
Ali Campbell has since toured as part of the breakaway group UB40 Featuring Ali, Astro & Mickey.