Her partner Charlie Rowley, 45, is still in a critical condition after the couple fell ill last Saturday.
Rowley, 45, remains critically ill in hospital.
Police suspect Rowley and Sturgess handled an item from the first attack, which Britain blames on Russian Federation.
British police say a woman who was exposed to a nerve agent in southern England has died.
"Dawn leaves behind her family, including three children, and our thoughts and prayers are with them at this extremely hard time", Assistant Commissioner Neil Basu, head of UK Counter Terrorism policing, said Sunday.
Britain maintains the March attack on the Skripals had been ordered by the Russian government, a charge denied by representatives of Russian President Vladimir Putin.
Russia, which is now hosting the soccer World Cup, has denied any involvement in the Skripal case and suggested the British security services had carried out the attack to stoke anti-Moscow hysteria.
Theresa May said she was "appalled and shocked" by the death, which comes after the poisoning of Sergei Skripal and his daughter Yulia in Salisbury.
The investigation is being led by detectives from the Counter-Terrorism Policing Network and about 100 detectives are working on the case alongside Wiltshire Police. Ms Sturgess has since died in hospital.
Mrs May sent her "thoughts and condolences" and said officials are "working urgently to establish the facts".
The new poisoning has frightened some residents who thought an extensive cleanup had removed the threat of any further Novichok exposure.
Authorities later determined that both people had been exposed to Novichok, a military-grade nerve agent produced by the Soviet Union decades ago.
Sergei Skripal and his daughter, Yulia, almost died of exposure to Novichok left on the front doorstep of Sergei's home in March. "Understandably, this is likely to raise the level of concern in Amesbury and Salisbury".
Britain's public health authority acknowledged on Friday the concerns of people living in the area after the two incidents involving Novichok, but said it was confident that the risk to the public remained low. Police said there is no evidence that either Sturgess or Rowley visited any of the sites where the Skripals may have been poisoned.
John Glen, the MP for the region, said the new poisoning has threatened an economic rebound from the slowdown caused by the attack on the Skripals.