At least 17 Turkish employees of a company building a football stadium were kidnapped in the Sadr City area of north Baghdad on Wednesday, security officials said.
A police colonel said that 17 Turks were kidnapped by black-clad gunmen in pickup trucks, while an interior ministry official put the number seized at 18.
The colonel said those kidnapped included three engineers as well as employees of the administrative department and labourers.
Neither official identified the company, but the website of Turkey's Nurol said it had been awarded a "design-build contract" for a 30,000-seat Sadr City Stadium.
The project also includes practice fields and a hotel, it said.
Kidnappings for ransom are a persistent problem in Baghdad, and the identity of the kidnappers was not immediately clear.
A political motive is also possible, as Sadr City is a stronghold of pro-government Shiite militias battling the Islamic State jihadist group, which overran large areas of Iraq last year.
Ankara has been accused of complacency towards IS and complicity in assisting the jihadist group, which also holds substantial territory in Syria, just over Turkey's southern border.
Turkey has carried out limited strikes against IS in Syria, but in an indication of its priorities, has directed far more firepower against the rebel Kurdistan Workers' Party (PKK).
Relations between Baghdad and Ankara have been rocky for years, with the two sides differing over Turkey's decision to help Iraq's autonomous Kurdish region export oil independently, and the civil war in Syria.
But ties have improved somewhat since Prime Minister Haider al-Abadi took office last year, replacing Nuri al-Maliki, who had repeatedly clashed with Ankara.