Turkey and the US have become embroiled in a consular row, mutually suspending most visa services.
The Turkish embassy in Washington said it needed to “reassess” the US government’s commitment to the security of the mission and personnel.
A very similar statement was earlier made by the US embassy in Ankara.
Washington condemned the move as baseless and damaging to bilateral relations.
The arrested consulate employee was a male Turkish citizen, Turkey’s state-run Anadolu news agency reported.
In its statement on Sunday, the Turkish embassy in Washington said: “Recent events have forced the Turkish government to reassess the commitment of the government of the US to the security of the Turkish mission facilities and personnel.
“In order to minimise the number of the visitors to our diplomatic and consular missions in the US while this assessment proceeds, effective immediately we have suspended all visa services regarding the US citizens at our diplomatic and consular missions in the US.
“This measure will apply to sticker visas as well as e-visas and border visas.”
The Turkish statement is virtually the same as the earlier American one, with only country names being replaced.
The American mission said that “all non-immigrant visa services at all US diplomatic facilities in Turkey” had been suspended.
Non-immigrant visas are issued to those travelling to the US for tourism, medical treatment, business, temporary work or study.
Those seeking citizenship or permanent residency apply for US immigrant visas.
Ankara has for months been pressing Washington to extradite US-based cleric Fethullah Gulen over his alleged role in the coup attempt in July 2016.
Turkish President Recep Tayyip Erdogan accuses Mr Gulen of instigating the unrest – a charge the cleric denies.
In the aftermath of the coup attempt, which was led by military officers, 40,000 people were arrested and 120,000 sacked or suspended.