Asda in Fratton has been cordoned off by officers from Hampshire Constablary.
Vehicles attempting to enter the site are being turned away by officers.
The area was thrown into lockdown just after 1.30pm in Tuesday follows the store computer systems that run the tills crashed throwing the store into chaos.
Police are understood not have been called to prevent a breach of the
Asda have been approached for a fix on when they expect their systems to be restored.
A spokesman said that they have engineers working to correct the problem.
Hampshire Constablary have been approached for comment
More to follow