The shots were fired from a white vehicle at the security booth outside Gate 6, Fox News reports.
The US embassy in Ankara and the consulate in Istanbul have been the targets of attacks by militants, besides receiving threats in the past.
Turkey's economy, and its currency in particular, has been shaken by United States sanctions created to force the release of detained American pastor Andrew Brunson.
USA embassy spokesman David Gainer would only confirm that a "security incident" took place.
USA administration had imposed sanctions and vows to do more against Turkey in the case the pastor would not be released immediately. "We have no reports of any injuries and we are investigating the details", said David Gainer, the embassy spokesman.
In a Twitter post, Ibrahim Kalın said: "We condemn the attack on the USA embassy".
"We thank the Turkish National Police for their rapid response", he added.
The statement said the investigation was ongoing and the suspect or suspects have not yet been identified. While the security officials have gathered cartridges and other evidence from the spot.
A police officer said several gunshots were fired about 5 am (0200 GMT) and that nobody was hurt where the embassy is closed this week due to the Islamic Eid al-Adha holiday.
Evangelical pastor Andrew Craig Brunson -currently under house arrest after more than 1½ years in prison- is facing up to 35 years in prison if convicted of espionage and terror-related charges.
Turkish President Tayyip Erdogan speaks during the sixth Congress of the ruling AK Party (AKP) in Ankara, Turkey, August 18, 2018. U.S. President Donald Trump has called for his immediate release. Turkey has also increased imports tariffs on some products.