The Anadolu state news agency said Hakan Demir, head of the leftist Birgun website, was detained for "inciting the people to hatred and enmity" over a message on Twitter.
Birgun was heavily criticised online after reporting that civilians were killed in Turkish strikes against Kurdish positions in Syria on Wednesday, which was denied by the government.
Police said they had opened a total of 78 cases against individuals for "propaganda" online against the operation.
Turkey launched "Operation Peace Spring" on Wednesday against the Kurdish-led Syrian Democratic Forces, which it considers a "terrorist" offshoot of Kurdish insurgents in its own territory.
It has arrested online critics during previous offensives against Kurdish forces in Syria, accusing them of "terrorist propaganda".
Rights groups criticise the erosion of free speech under President Recep Tayyip Erdogan, particularly in the wake of a failed coup in 2016 which was followed by tens of thousands of arrests of political opponents.