The appeals court upheld a ruling made at the district court in Hillerød in April.
Authorities in Rwanda have accused the man, whose identity was not disclosed, of participating in the killing of some 2,000 people who had sought refuge in a church and a university in Mutende.
Witnesses have described how the accused walked around the church with his dog looking for Tutsis.
He is accused of killing an elderly woman and an infant, as well as three youths at a roadblock.
The man has denied the allegations and argued that Rwandan authorities have
confused him with someone else.
The man left Rwanda in 1997 before arriving in Denmark in 2001. He was granted residency in 2002 and became a Danish citizen in 2014.
Danish police were tipped off about the man, who now has four children in Denmark, more than a decade ago, according to Danish news agency Ritzau.
Danish investigators travelled to Rwanda and interrogated more than 30 witnesses in their probe.
After investigating the case and corresponding with Rwandan authorities for several years, the man was arrested in May 2017.
The 1994 genocide in Rwanda saw 800,000 people, mainly minority Tutsis, slaughtered by the military and Hutu militias.