The Brazil international, who was injured in Friday's league game against Rostov, will be sidelined for up to two weeks, the Russian champions said on their website.
Hulk's injury is a major blow to Luciano Spalletti's team, who are third in Group C with three points, two points above Anderlecht after beating the Belgian champions 1-0 last month in St Petersburg.
The powerful forward has been Zenit's top scorer since joining them for a Russian league record 60 million euros just before the transfer deadline.
Hulk will also miss Brazil's friendly against Colombia in the United States next Wednesday.
- Sports & Recreation
- Luciano Spalletti