The Danish badminton star won convincingly 21-13, 21-18 over the Indonesian Alwa Farhan, who is ranked 40 in the world.
Axelsen, who needed three sets on Wednesday to advance from his opening match in Germany, cruised along on Thursday.
In the first set, Farhan played well in the opening stages and took the lead 10-9. But from there, Axelsen won eight points in a row, to take a 17-10 lead.
The match pattern repeated itself in the second set, where Farhan took the lead 11-10.
Axelsen, who is currently ranked four in the world, then grabbed five points in a row and made it 15-11, against the Indonesian who visibly lost his belief that he would be able to turn the match around.
Even though Farhan saved four match points in the end, there was never any real doubt about the win.
In the quarter-final, Axelsen was expected to face fellow countryman Rasmus Gemke, but Gemke had an off-day and lost in three sets to Jason Gunawan from Hong Kong.
Gemke, who is number 29 in the world, lost 11-21, 21-15, 13-21 to Gunawan who is ranked 42 in the world.