Winslow has been suspended by the NFL for testing positive for a banned substance and will miss his side's next four games starting with their clash with the Pittsburgh Steelers.
"It came as a huge surprise to me when I learned that I tested positive for a banned substance," Winslow told ESPN.
"I have investigated all possible sources since learning of the positive test, including possible medical causes but frustratingly, I do not know the source. I do not take supplements that list any banned ingredients, but NFL policy is very strict so I am accountable for the results.
"I sincerely apologise to my teammates, coaches and Jets fans for this situation I will work extremely hard during this time away from the field and look forward to contributing as soon as the suspension ends."
The Jets are 3-2 in their season going into week six.