The company said it had a "temporary network issue" which affected calls and texts during Saturday afternoon and evening.
It said calls had since been restored and that it is working to restore full service.
But some users on Twitter complained of their texts being sent to random numbers instead of their contacts.
A spokeswoman said the company was "currently investigating the cause of the service disruption" and that it apologised for any inconvenience.
It also said that some "customers and non-customers" may have received a message from an unknown sender on Saturday.
In a statement on its website, the company said its advice "is to ignore all text messages that you deem incorrect".
Three, which has about nine million customers, experienced a data breach last year which saw personal details, including names and addresses, accessed unlawfully.
Sign-up to get news from the BBC in your inbox, each weekday morning

Watson, 22, is charged with an "act contrary to good sportsmanship", as well as tackling Alex Goode in the air.
The first offence alleges he used "offensive, inappropriate and unprofessional" language after being sent off.
Watson featured in every Six Nations game for England this year as they won their first Grand Slam since 2003.
England tour Australia in June and Watson's place may be in doubt if he is found guilty of a dangerous tackle at a hearing on Tuesday, with the charge carrying a top end sanction of 10 weeks.
If found guilty, the minimum punishment is a two-week suspension.
Former London Irish player Watson could face penalties ranging from a reprimand, to a financial penalty, or a suspension if he is found guilty of the unsportsmanlike conduct charge.
Bath - beaten finalists last year - are ninth in the Premiership table with four games left to play this season.

People for the Ethical Treatment of Animals (Peta) wants the mascot to be replaced with a modern animal-friendly version.
The group has suggested a fish with the slogan Skegness - A Happy Plaice.
The mayor of Skegness said all suggestions were welcome but said he did not think there would be much support for Jolly to be axed.
The original Jolly Fisherman poster was commissioned by the Great Northern Railway to encourage visitors to take the train on their seaside breaks to Skegness.
The poster featured the slogan "Skegness is so bracing".
It was commissioned in 1908 for 12 guineas and has became synonymous with the Lincolnshire resort.
However, Dawn Carr, of Peta, said Jolly "evokes images of cruelty to animals".
"Fish being tricked into impaling themselves in the mouth, animals being pulled out of the ocean in giant nets where they are so crushed together the pressure pushes their stomachs out through their mouths and their eyes pop out."
"This is what the Jolly Fisherman represents," she said.
She said Peta's suggestion would give the resort an opportunity to rebrand itself as a progressive holiday destination.
"One where the mutilation and killing of sea animals is not being celebrated."
Skegness's mayor, Carl Macey, said the Jolly Fisherman was loved by adults and children alike.
He said: "Animal cruelty is something we don't want to be portrayed for, but I don't feel Jolly has ever come across in that manner.
"He is just accepted as happy and friendly and he does such a wonderful job for Skegness.
"It [Peta's suggestion] will go before council, but if it isn't broken we won't try and fix it."
Mobile phone company Three has apologised after some of its customers were unable to make calls or texts.
[NEXT_CONCEPT]
Bath full-back Anthony Watson faces two Rugby Football Union charges after being sent off in the loss to Saracens.
[NEXT_CONCEPT]
An animal rights group is calling for the Skegness mascot, the Jolly Fisherman, to be replaced with a fish.