The Dutch National Police Corps has not identified the pilot but says he is a 52-year-old captain from Woodbury, N.J., according to the Associated Press.
Delta issued a statement about Flight 35, saying that it was "cancelled out of concern that a crew member appeared to be unfit for duty."
"Local Amsterdam authorities have met with the crew member to begin their investigation and we are cooperating fully, while simultaneously launching our own internal investigation," Delta said in a statement. "The crew member has been suspended pending the outcome of these investigations. Impacted passengers have been reaccomodated on other flights."
Delta pilot policy specifically tells pilots not to report for duty with the presence of any amount of alcohol in their system.
"Our policy is among one of the strictest in the industry and we have no tolerance for violations," Delta spokesman Anthony Black.
Police say they arrested the man in the cockpit of his plane after an anonymous tip. The AP reported that a breath test found he had a blood alcohol content of 0.023 percent - a hair above the legal limit in the Netherlands.
The pilot was fined about $900 and released, according to a statement from police.