Drone debris also damaged several buildings in the city, including a school.
Ukraine’s prosecutor general identified the shooter as a 58-year-old Russian who stays in Ukraine.
EU leaders will meet in Brussels on Thursday, aiming to agree on how to fund Ukraine’s economic and military needs in the coming years.
No details of the allegations against Mr Galushchenko have been provided by authorities.
President Volodymyr Zelensky said Russia lacked the strength to mount large-scale new offensives, citing heavy troop losses after more than three and a half years of war.
Mr Zelensky also criticised China for hosting Mr Putin during his recent four-day state visit.
Messrs Putin and Zelensky have not met since December 2019.Â
Mr Zelensky proposed a meeting to take place later this week, with no finalised date yet.
It is Mr Zelensky’s first visit to Austria since the start of Russia’s all-out invasion of Ukraine in February 2022.
Mr Zelensky urged the U.S., Europe “and others around the world who called for an end to the war’’ to act.
