Band member Alex Turner has been diagnosed with laryngitis and is unable to perform as scheduled at the Hydro tonight, a statement said.
Instead, they now plan to take to the stage on Thursday, November 21, at the same venue.
The band made the decision after postponing their Birmingham LG Arena show, last night. This will take place on Wednesday, November 20.
All tickets will remain valid for these shows.
A statement, released by Scottish promotor DF Concerts, read: "We wish to apologise to all ticket holders for any inconvenience this has caused.
"Please contact the customer services at the box office you purchased your tickets for any further assistance."