Scans revealed the founder member of the band, which formed in Birmingham, has two tumours after he suffered a seizure at home on 19 March.
He will undergo surgery on the day he was due to begin the tour.
The musician said he would "be there in spirit" and the only thing left on his bucket list was returning to music.
UB40 confirmed the tour, starting on Friday in Portsmouth, would go ahead in Travers' absence.
