The outage comes as households wait to hear about a rise in water charges on Thursday morning.
Ofwat, the water regulator, is expected to announce that charges will increase for those in England and Wales by more than 20% over the next five years.
Southern Water said the problem in Hampshire had been caused by a “technical issue” at its Testwood Water Supply Works, resulting in low pressure or a loss of water supply.
It added that bottled water stations were being set up and it was continuing to deliver them to customers on its priority list.
Stations have opened at Places Leisure Centre – formerly Fleming Park – in Passfield Avenue, Eastleigh, and the Lordshill Sainsburys in Southampton.
Southern Water said tankers were also pumping water directly into the network to help reduce the impact.
Three of them had been dedicated to Southampton General Hospital, which is also being affected.
The lack of water also caused more than 20 schools to shut, including North Baddesley Infant School and Halterworth in the Test Valley, and The New Forest Academy, Cadland Primary School and Wildground in the New Forest and Mountbatten school Romsey.
Southern Water said it had contacted all of them.
