The British number one had been closing in on his third title of the year but complained of jetlag after beating Japan's Kaichi Uchida in the last 16.
The 27-year-old is the third player to withdraw from the tournament this week, following the previous exits of Borna Coric and Taylor Fritz.
Norrie's withdrawal puts his participation in next week's Japan Open in doubt and could hit his hopes of pushing towards a place at the season-ending ATP Tour finals.
Britain's Liam Broady, who had been enjoying one of the best weeks of his career at the Tel Aviv Open and beat 35th-ranked Botic Van De Zandschulp on Thursday, was also forced to withdraw just before his scheduled quarter-final against second seed Marin Cilic.
No reason for the retirement was initially given.