Campaigners blocked the tracks and some have even tried to climb overhead line equipment, National Rail said.
Crowds are holding banners which read “Stop Turkey from helping ISIS terrorists”.
The demonstration follows several months of conflict between Kurdish groups and Turkish forces in Afrin, northern Syria.
Turkey regards the YPG as a terrorist group, although it is not a proscribed organisation.
Red flags displaying the emblem of the proscribed PKK are also visible in images of the Manchester Piccadilly protest posted to social media.
Network Rail said train services may be “amended, cancelled or delayed by up to 60 minutes”, adding “major disruption” is expected until 17:30 GMT.
British Transport Police are at the scene after officers were called to the station shortly after 13:00 GMT.
Some passengers have been left angry by the disruption caused by the protest.
Went to get a train from Manchester Piccadilly station – it’s on complete shutdown due to a protest on the tracks. Just shared a taxi with 3 Stockport strangers: we discussed Turkey, human rights & non violent direct action. So 🙌🏻 to a successful disruptive protest! 👊🏻 pic.twitter.com/L9CsDMTEZS — G 💅🏻 (@geeriggle) March 11, 2018