Engineers are said to have been dispatched and are investigating the source of the problem.
However, Mr Hunt called for a water pumping station to be considered “ASAP” and said the company should consider giving out bottles of water to residents.
In November, a similar outage left 12,000 people with no fresh water for days on end. Tankers were deployed to the area to provide supplies.
Alan Cochrane, Thames Water’s co-chief executive, said in a statement on Tuesday: “I’m really sorry if you’re experiencing low pressure or no water – I know how disruptive and inconvenient this can be, especially on Boxing Day.
“Our specialist engineers have now arrived in GU4 and are working hard to get your water supply back to normal as quickly as possible.
“As soon as we have an update, we’ll let you know how soon we’ll get things back to normal.
“Thank you for your patience, and again, I’m very sorry for the disruption to your day.”
Mr Hunt tweeted: “Have now heard back from both acting CEO’s of Thames Water.
“Al Cochran says it is affecting GU4 and GU5 postcodes. There is an engineers investigation going on right now and they will keep me posted.
“But I have to say I am beside myself with frustration that this is happening *again* and over Christmas.
“If this is going to take any time at all we need a water station up and running asap.”
In a tweet directed at constituents, Mr Hunt added: “I know many of you are hosting friends and family and this water outage is hugely inconvenient.
“Following your requests I have raised the question of bottled water in impacted areas and also requested [Thames Water] ensure vulnerable people are looked after.
“I am aware a number of you are having problems getting through on the TW hotline – also raising this with [Thames Water]“.