The singer is taking time to rest on doctors' orders after being diagnosed with an upper respiratory infection, which had already caused her to cancel a recent Paris gig.
Houston had been scheduled to kick off her UK tour by performing in Manchester on Thursday and Friday this week, but the dates will now take place on June 16 and 17.
Meanwhile, a Glasgow show which was planned for Sunday has been pushed back until May 1.
Houston's record label RCA said: "Doctors visited Whitney late last night in Paris and confirmed that she was suffering from an upper respiratory infection. Upon medical advice, Whitney has been advised that she cannot perform to allow her time to recover."
The rest of the star's tour dates are currently expected to go ahead as planned.