Valeria Gontareva was also injured last month when she was knocked down by a car in London, where she now lives.
Ms Gontareva fears she is the victim of a campaign of harassment linked to her decision in 2016 to nationalise Ukraine’s largest commercial bank.
“I have no evidence, but I think it’s linked,” she said.
Ms Gontareva told the BBC she had “received many threats” that contained references to her
The former owner of Privatbank, Ihor Kolomoisky, earlier rejected claims that he may be connected to the threats, telling reporters at the weekend that Ms Gontareva had many enemies.
He also said he found it hard to believe that there had been any threats against Ms Gontareva. “Where would you see a person who has been threatened talking openly [about it] in interviews with major news outlets?” he told Ukrainian news website Novoye Vremya.
Ukrainian President Volodymyr Zelensky described the arson attack as a “provocation” and urged the country’s law enforcement agencies to act swiftly.
Ms Gontareva, speaking on Tuesday by phone from a wheelchair in London, listed what she had been subjected to over the last month: hit by a driver as she walked across a pedestrian crossing in Knightsbridge, her son’s car set on fire, her apartment in Kiev raided and now her house just outside the Ukrainian capital targeted by arsonists.
When Privatbank was nationalised in 2016, more than $5bn (€4.5bn; £4bn) of taxpayer money was pumped into the bank, which was deemed too important to Ukraine’s economy to be allowed to fail.
Financial investigators blamed the bank’s former owners, like Mr Kolomoisky, saying they had undertaken “related party lending” on a massive scale.
Mr Kolomoisky denied any wrongdoing, but facing numerous court cases he chose to spend most of the last three years living in self-imposed exile in Switzerland and Israel.
Then this year Mr Zelensky, a comedian whose shows are often broadcast on Mr Kolomoisky’s television channel, surprised many Ukrainians when he was elected president.
One of Mr Kolomoisky’s lawyers became President Zelensky’s chief of staff, and the oligarch was suddenly back on the scene in Ukraine.
Last weekend, Mr Kolomoisky attended an international conference and was photographed holding talks with Mr Zelensky at the presidential administration.
There has been widespread speculation that the oligarch might be trying to negotiate compensation for the loss of Privatbank.
If that were to happen it would be a hammer-blow to President Zelensky’s claims to be a reformer, and could irreparably damage his relationship with both international donors and the International Monetary Fund (IMF).