The embassy said "recent events" had forced the US government to reassess Turkey's "commitment" to the security of US mission services and personnel in the country.
In order to minimise the number of visitors while the assessment is carried out, "effective immediately we have suspended all non-immigrant visa services at all US diplomatic facilities in Turkey," it said.
Non-immigrant visas are issued to all those travelling to the United States for tourism, medical treatment, business, temporary work or study. Visa services are only those seeking to live in the US permanently.
The employee was remanded in custody by an Istanbul court late on Wednesday on accusations of links to the group of US- based preacher Fethullah Gulen, blamed by Ankara for last year's failed coup against President Recep Tayyip Erdogan.
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The man has been formally charged with espionage and seeking to overthrow the Turkish government.
The embassy on Thursday said it was "deeply disturbed" over the arrest and rejected the allegations as "wholly without merit".
But Erdogan's spokesman Ibrahim Kalin has defended the arrest, saying "there must be serious evidence" and pointing to a phone call made from the Istanbul consulate to a key suspect on the night of the coup.
The issue has added yet another bone of contention in the increasingly troubled relationship between Washington and Ankara.
Turkish officials had expressed hope of a new page in Ankara-Washington relations under President Donald Trump.
The lack of movement on the issue has further strained ties already fraying over Washington's support for a Syrian Kurdish militia Ankara deems to be a terror group.
Meanwhile, members of Erdogan's security detail were indicted by US authorities after clashes with protesters during an official visit this year, infuriating the Turkish president.
American pastor Andrew Brunson, who ran a church in the western city of Izmir, has been held by Turkish authorities since October 2016 on charges of being a member of Gulen's group.