Journalist Darya Dugina, aged 29, died on Saturday when a vehicle she was driving exploded near Russia's capital.
Her prominent ultra-nationalist father, Alexander Dugin, said to be close to Mr Putin, may have been the intended target of the attack.
Ukrainian officials have denied any involvement in the explosion.
But Russia's Federal Security Service (FSB) said on Monday it had solved the case and said that Ukraine was directly responsible.
The FSB told Russian media that a Ukrainian woman had moved to Russia in July alongside her young daughter - but that she was in fact a Ukrainian special services contractor.
The woman, it said, rented an apartment in the same building as Ms Dugina for a month, preparing for the attack. In that time, she allegedly followed the journalist through Moscow in a Mini Cooper - for which she used three different licence plates.
The suspect then escaped to Estonia after the explosion, the FSB said.
An adviser to Ukraine's President Zelensky, Mykhailo Podolyak, said the FSB's version of events was "Russian propaganda" from "a fictional world".
The FSB later released video of the accused's car entering Russia, security footage of her entering what is said to be Ms Dugina's building, and leaving Russia.