The Paisley-born singer had already cancelled the SSE Hydro arena gig on Monday night as part of a UK-wide tour.
It had been hoped he would play his second date at the SECC venue on Tuesday night but that has now been called off on medical advice.
Promoters said fans with tickets should keep them and look out for the rescheduled dates.
Scots singer Paolo Nutini has postponed his second Glasgow show after being diagnosed with severe tonsillitis.