The family also thanked all the staff at Salisbury District Hospital who treated her, and sent their "thoughts and prayers" to Mr Rowley and his family.
Dawn Sturgess, 44, died in hospital at the weekend and her partner Charlie Rowley remains critically ill in hospital.
Police seized a auto in the large town of Swindon as part of their probe into the death of 44-year-old Dawn Sturgess, who was exposed to Novichok, a military-grade nerve agent produced in the Soviet Union during the Cold War.
Defence Secretary Gavin Williamson blamed Russian Federation for committing "an attack on British soil" over the latest poisonings, some four months after Sergei and Yulia Skripal were targeted.
Meanwhile, Ms Sturgess' family have paid tribute to the mum-of-three.
In a statement, they said: 'Dawn's death has been devastating for us.
I want to emphasise to everyone in the Salisbury and Amesbury area that nobody, adult or child, should pick up any foreign object which could contain liquid or gel, in the interests of their own safety.
'She would do anything for anybody and those who knew Dawn would know that she would gladly give her last penny to somebody in need.
Last night police seized a auto in Swindon in connection with the Novichok poisoning in Amesbury.
A bus used by Mr Rowley and Ms Sturgess the night before they got ill has also tested negative for novichok.
His auto was sealed and taken away on the back of a truck.
Residents also claimed he had told them both his auto and his clothes were being taken to the government laboratory at Porton Down to be destroyed.
"We have arranged the transportation of a vehicle from an address in Swindon this evening in relation to the on-going incident in Amesbury", said Wiltshire Police.
The BBC understands Mr Rowley's flat is regarded as the key location in the search.
Police are yet to recover that item but Public Health England said the risk to the public is low and warned against picking up "any odd items such as needles, syringes or unusual containers".
A police cordon remains outside Charlie's house, while officers have also sealed off Rollestone Street in Salisbury, where Dawn had been living at John Baker House.
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