Darya Trepova, 26, was earlier placed on the interior ministry's wanted list and her arrest was later confirmed by Russia's Investigative Committee.
Russian media reported that Tatarsky was passed a statuette shortly before the blast, and there is speculation a device could have been hidden inside.
Dozens of other people were wounded.
Videos posted on social media showed an explosion and people wounded on the street.
Russian authorities say they are investigating the attack in the centre of Russia's second biggest city as a "high-profile murder".
Ms Trepova was detained hours after her mother and sister were brought in for questioning, Russian news agencies reported. She had been reportedly detained for a number of days after an anti-war protest in February last year.