Fullkrug picked up the injury during training with the Hammers before pulling out of Germany's national team selection earlier this month.
Speaking to DAZN Portugal on Thursday, Nuno admitted the striker's recovery could take a while, leaving the team short of options up front.
"Fullkrug will be out for some time," Nuno said. "For this specific position, we have Callum Wilson, and we also have a young kid, Callum Marshall, who already came on in the last game. But we will have to find solutions as a team."
The 32-year-old German has endured a difficult spell since joining West Ham from Borussia Dortmund in a twenty-seven million pounds deal last summer.
He missed several games last season through injury and is still yet to score for the Hammers this campaign.
Fullkrug's absence could open the door for 20-year-old academy graduate Marshall, who made his Premier League debut in the 2-0 defeat to Arsenal. Nuno has been impressed by the youngster's attitude in training and showed faith in him by introducing him ahead of Wilson during that match.
Wilson, meanwhile, has struggled with his own fitness issues, but he remains the most experienced forward available as West Ham prepare to face Brentford at London Stadium on Monday, 20 October.
Nuno, who started Fullkrug in each of his first two matches as head coach, will now be forced to adjust his attacking approach for his first home game in charge.
With Fullkrug's latest setback adding to his ongoing fitness troubles, the Portuguese manager must rely on Wilson's experience and Marshall's energy to keep West Ham's frontline firing.