The 60million euros record signing picked up a hamstring injury in the first half of Zenit's 2-1 Premier League win over Rostov on Friday, and the club confirmed he will subsequently be out of action for two weeks.
Hulk has been a revelation since his big money move from Porto over the summer and has been their leading scorer this season.
The 26-year-old Brazilian's absence will be keenly felt as Zenit once again attempt to beat Anderlecht, who were defeated by Aleksandr Kerzhakov's late penalty when the sides met in Russia two weeks ago.
Head coach Luciano Spalletti will hope that win can kickstart Zenit's European campaign after they had suffered a heavy defeat at Malaga before being edged out by AC Milan at home in their previous matches.
Danny is likely to be on the bench for Zenit after making his first appearance in 11 months against Rostov at the weekend following a cruciate knee ligament injury.
Anderlecht, rock bottom of Group C with just one point from their opening three matches, will surely need all three points if they are to keep their slim hopes of progression alive.
History is against them, however, and they will be searching for a first win in eight years at the Constant Vanden Stock Stadium in this competition.
The Belgian champions have lost eight and drawn two of 10 group matches in the Champions League although the last time they welcomed Russian opposition they won, with Lokomotiv Moscow beaten 5-3 last December in the Europa League group stages.
Coach John van den Brom has taken comfort from their recent league form following heavy wins over AA Gent and KV Mechelen since their last European outing.
"This was a nice week and the next week can even become more beautiful. The big victories give us a lot of confidence," Van den Brom said in the Het Nieuwsblad newspaper. "We are ready to hurt the Russian side on Tuesday."
Dieudonne Mbokani will play with a protective mask due to a broken nose, while late decisions will be made on Olivier Deschacht and Ronald Vargas, but Behrang Safari is fit.