Zenit said the 26-year-old Russian tore the anterior cruciate ligament of his right knee in Thursday's Europa League Round of 16 tie against RB Leipzig, a 1-1 home draw in the second leg which meant the Germans advanced 3-2 on aggregate.
The Russian national team has already lost defenders Viktor Vasin and Georgy Dzhikiya since the start of the year to major knee injuries.
Korokin, who is the second top-scorer in the Russian Premier League with 10 goals, was called up to the national team last year after being snubbed for nearly a year due to poor performances and off-pitch scandals.
The forward and Russia team mate Pavel Mamayev were demoted to their club reserve teams after footage of them at a champagne-fuelled party in Monaco emerged online following the country's early exit from the 2016 European Championship.
Kokorin, who did not play in last year's Confederations Cup, stirred more controversy by posting a video on Instagram in which he and striker Artem Dzyuba mocked national team manager Stanislav Cherchesov after Russia's elimination from that tournament.
Russia will host the World Cup at 12 venues spread across 11 cities including Moscow, St Petersburg, Kazan and Sochi. They have been drawn in Group A alongside Saudi Arabia, Egypt and Uruguay.
(Reporting by Gabrielle Tétrault-Farber; Editing by John O'Brien)
