The former The Smiths frontman called off several gigs on his North American tour last month after being admitted to a US hospital for treatment, with a spokesman blaming a bleeding ulcer.
It subsequently emerged the veteran rocker had been diagnosed with Barrett's esophagus, an abnormal change in cells in the throat which is linked to a significantly increased risk of cancer - but Morrissey vowed to be back onstage in Las Vegas on 9 February.
However, the star has now axed Saturday's concert, as well as his Sunday appearance in Phoenix, Arizona, to focus on his health.
A post on his Facebook page reads: "Due to doctor's orders, the upcoming engagements with Morrissey in Las Vegas on Sat Feb 9 and in Phoenix on Sun Feb 10 will need to be rescheduled.
"Morrissey is currently undergoing treatment for a bleeding ulcer and Barrett's esophagus. These shows are in the process of being rescheduled immediately... Morrissey thanks everyone concerned for their well wishes during this time and hopes for a speedy recovery."
It is hoped the tour will now resume in El Paso, Texas on 12 February.