Irene Nel was instructed on Tuesday afternoon by board chairperson Judge Jack Moloi to avail herself to testify at 10:00. However, the Durban woman had not arrived by 11:00.
Moloi issued the instruction after evidence leader advocate Viwe Notshe requested a postponement to next week Tuesday, citing Nel's unavailability.
He also said his team was still trying to trace two other witnesses - one of whom had been suspended by the department of public works.
Moloi declined the request, and adjourned the hearing to later on Wednesday.
Nel is expected to testify about compliance or non-compliance with supply-chain management prescripts in a planned lease for the Transnet building in Durban.
On Monday, Vincent Maleka SC, for Cele, said his client would tell the board he had raised issues relating to the police's future accommodation because he knew the lease contract at Servamus was ending.
The board was appointed by President Jacob Zuma last October.
Its brief is to determine whether Cele acted corruptly or dishonestly, or with an undeclared conflict of interest in relation to two leases for police office space.
It will also examine Cele's fitness to hold office and his capacity to efficiently execute his duties.
Public Protector Thuli Madonsela's report, which found Cele's action pertaining to leases for new police headquarters in Pretoria and Durban, valued at R1.6bn, was "improper and unlawful", was instrumental in the board's establishment.
Her finding will form part of evidence at the inquiry.