The 29-year-old from Aarhus defeated Belgium's Julien Carraggi 21-11, 21-10 in the first round.
The two know each other from their time together playing for the same club in Hvidovre, an advantage Gemke was able to capitalize on.
He outperformed his opponent in every aspect of the game; after the score was tied at 2-2 in the first set, Gemke steadily pulled away.
Carraggi, ranked 48th in the world, appeared disheartened by the Dane's dominance and was effectively outplayed. Gemke is ranked 26th globally.
Gemke will face much tougher opposition in the second round when he takes on the 12th-seeded Lin Chun-yi from Taiwan.
The mixed doubles pair of Kristoffer Kolding and Mette Werge also advanced to the second round on Tuesday, defeating a Swedish duo 21-19, 21-16.
In the second round, they will face the fifth-seeded French pair, Thom Gicquel and Delphine Delrue.
Denmark's highest-ranked men's doubles pair, Daniel Lundgaard and Mads Vestergaard, played their first match of the championships later in the day.
After receiving a bye in the first round as the 13th seeds, Lundgaard and Vestergaard defeated a Brazilian pair 21-14, 21-11 in the second round. A Chinese pair awaits them in the third round.