Joe Robinson, who lives in Leeds, was detained along with his girlfriend and her mother while the trio were on holiday.
It has been reported the two women have since been released, but 23-year-old Mr Robinson remains in custody.
Mr Robinson,formerly of Accrington, Lancashire, fought alongside the People's Protection Units of Syrian Kurdistan (YPG) against terror group IS.
But Turkey is hostile to the YPG because of links with the Kurdistan Workers' Party, which is fighting for Kurdish autonomy in Turkey,
The Kurdistan Solidarity Campaign said: "Unfortunately, Joe has gone on holiday to Turkey not realising the kind of state it has now become.
"Turkey unfortunately continues to criminalise the Kurdish question and has jailed tens of thousands of Kurdish people, including elected MPs and mayors simply for peacefully campaigning for Kurdish rights.
A Foreign Office spokeswoman said: "We are aware of the detention of a British national in Turkey and have requested consular access."