The 26-year-old world number 49 took the first set 7-6 (7-5) against American Sam Querrey, having saved four break points.
The second set also went to a tie-break, which Querrey won 7-6 (10-8), but then Bedene withdrew when trailing 2-1 in the third.
The Briton had lost a three-hour semi-final in Chennai, India on Saturday.
British number two Aljaz Bedene was forced to retire hurt in his opening match at the ASB Classic in Auckland.