The 170m-high viewing tower - built by Mowlem - was originally meant to open in time for the turn of the millennium but work eventually began in 2001. A series of problems has led to it opening almost five years late.
A spokeswoman for Heritage said an official was reportedly trapped inside.
Portsmouth City Council was criticised by the Audit Commission for the handling of the tower project, particularly in organising contracts with the developers.
The tower, originally titled the Millennium Tower, was not meant to have cost local council tax payers any money but so far Portsmouth City Council has paid £11.1 million towards construction.
The Millennium Commission provided £15 million for the project, with £5.8 million coming from original contractor Berkeley Homes and another £2.7 million of contributions in kind.