The former Port Vale striker has not featured for Leeds since damaging his ankle during the club's pre-season friendly against Slovan Liberec in the Czech Republic, and he received a two-year contract from Wise while on the treatment table four days before the start of the League One campaign.
Wise said: "I should hopefully have him back in four weeks, fingers crossed. He's very important to me."
Constantine was expected to be a first-choice striker at Elland Road this season after scoring 26 goals for Vale last year, but a combination of his ankle injury and the current form of Tresor Kandol and Jermaine Beckford is likely to see him occupy a place on the bench when he returns to full fitness.
Norwegian striker Tore Andre Flo has also found himself relegated to a sub's role after a succession of foot injuries, and Wise added: "Tore has to wait because knows about the two up front. He thinks they're unbelievable."