The suspect, identified by the initials Z.T. and nicknamed Laz Ziya by Turkish media, was arrested in Reyhanli in Turkey's southern Hatay province near the border with Syria, the provincial governor's office said on its website.
The body of 33-year-old Sarai Sierra, a married mother of two from Staten Island, was found in the ruins of Istanbul's old city wall last month after she was first reported missing in late January.
Sierra, who had been traveling alone, was killed by a blow to the head.
After questioning Sunday, the man was handed over to judicial authorities, the governor's office said. It gave no further details.
Sierra's killing has attracted wide media attention the U.S. and in Turkey, a country which receives millions of tourists each year and is generally seen as a safe destination for foreign travelers.