The EBU, which produces the event, said Russia's inclusion could bring the competition into disrepute "in light of the unprecedented crisis in Ukraine".
Russia launched an attack on its neighbour Ukraine in the early hours of Thursday.
Western governments have ramped up international sanctions in response.
Last week, the contest had said Russia would be allowed to compete, so this is a rapid change in stance for the EBU.
It follows the announcement that football's 2022 Champions League final would be played in Paris, after Russia was stripped of the match following the invasion of Ukraine.
F1's Russian Grand Prix, due to take place in Sochi in September, was also cancelled.
Earlier last week, Ukrainian broadcaster UA:PBC urged the EBU to suspend Russia's Eurovision membership and ban it from the contest.
State broadcasters from countries including Iceland, Finland, Norway and the Netherlands had called for Russia to be banned from the contest.
Finland said if Russia took part, it would not send a representative to the contest in Turin in May.
Photo Getty Images Caption: Rock band Maneskin won last year's Eurovision and have gone on to score top 10 hits in the US, the UK and the rest of Europe