Ban said he was 'very disappointed' by the refusal and described it as a 'missed opportunity' for the regime.
Khin Moe Moe was originally scheduled to testify July 3, but the court session was postponed.
A special court was set up at Insein Prison to try Suu Kyi, beginning May 11, for breaking the terms of her detention by allegedly permitting US national John William Yettaw to swim to her lakeside home-cum-prison on May 3 and stay until May 5.
Critics have accused the military junta of using the case as a pretext to keep Suu Kyi in jail during a politically sensitive period leading up to a general election planned for next year.
That election would be the first since Suu Kyi's NLD won the 1990 general election by a landslide. It has, however, been blocked from power by Myanmar's junta for the past 19 years.
Suu Kyi has spent 13 of the past 19 years in detention.
The new trial of Suu Kyi, whose most recent six-year sentence under house detention expired May 27, has sparked a chorus of protests from world leaders and even statements of concern from its regional allies in the Association of South-East Asian Nations.