"This is not the end of her treatment but marks a significant milestone," Salisbury hospital's deputy chief executive Christine Blanshard said, adding that the 33-year-old Russian had asked for privacy.
She said that while Sergei Skripal, 66, is "recovering more slowly than Yulia, we hope that he too will be able to leave hospital in due course".
The pair were found collapsed on a bench in the south-western city of Salisbury on March 4 in what British authorities have said was attempted murder by the Russian state.
Western allies backed Britain but Moscow strongly denied any involvement, prompting a furious international row.
Countries around the world expelled more than 150 Russian diplomats in response, prompting Moscow to launch its own expulsions.
There were initially fears that the Skripals would not recover, but last week hospital and police officials said they were both improving.
In a short statement issued through police last week, Yulia Skripal said: "I woke up over a week ago now and am glad to say my strength is growing daily."
She said she had found the incident "disorientating", without providing any further details on the attack.
The following day, the hospital said her father was also "improving rapidly and is no longer in a critical condition".
The BBC reported that Yulia had been discharged on Monday and was moved to a secure location.
In a tweet, the Russian embassy in London said: "We congratulate Yulia Skripal on her recovery.
"Yet we need urgent proof that what is being done to her is done on her own free will."
'Responded exceptionally well'
Police have said they believe the Skripals came into contact with the nerve agent at Sergei Skripal's front door.
The former Russian military officer was recruited by British intelligence in the 1990s and later charged with treason in his own country.
However, he was pardoned in 2010 and moved to Britain as part of a spy swap between the United States and Russia.
His daughter was visiting at the time of the poisoning, the first offensive use of a nerve agent in Europe since World War II.
British scientists have identified the chemical as the Soviet-designed Novichok, although the international Organisation for the Prohibition of Chemical Weapons (OPCW) has yet to verify this.
A police officer among the first at the scene in Salisbury was also hospitalised, but was released on March 22.
Blanshard said nerve agents work by attaching themselves to particular enzymes in the body, which then stop the nerves from functioning, leading to sickness and hallucinations.
"Our job in treating the patients is to stabilise them, ensuring that they can breathe and that blood can continue to circulate," she said in a televised statement.
"We then needed to use a variety of different drugs to support the patients until they could create more enzymes to replace those affected by the poisoning.
"We also used specialised decontamination techniques to remove any residual toxins.
"Both patients have responded exceptionally well to the treatment we've been providing. But equally both patients are at different stages in their recovery."
