The 47-year-old was later released but had to surrender his passport to stop him returning to Syria.
Prosecutors said that Dutch law did not allow the use of force apart from in exceptional circumstances.
"Killing an IS fighter therefore could mean being prosecuted for murder," a statement from prosecutors said.
Even though the Netherlands is part of the international coalition against the so-called Islamic State (IS), the prosecutors said there was "an important difference between Dutch nationals who travel to Syria on their own to fight against IS and Dutch soldiers who train Iraqi and Kurdish forces".
The Dutch military presence was legal and took place "at the request of the Iraqi government", they added.
The man's name cannot be released under Dutch privacy law and it was unclear when he left the military.
Prosecutors said further investigation into the soldier's involvement was required to decide whether charges would be brought.
The BBC understands that about 100 Western volunteers have joined Kurdish forces in the region - including some Britons.
In some instances they have faced legal troubles on their return to their home countries.
One British former Royal Marine, Konstandinos Erik Scurfield, and one Canadian ex-soldier, John Gallagher, died in northern Syria in 2015 fighting Syria against IS militants.
A former Dutch soldier has been arrested on suspicion of killing Islamic State militants while fighting alongside Kurdish militiamen in Syria.