In response, the Iraqi forces launched a major search operation in northern Nineveh province and found the vehicle used in the attack, they said in a statement.
It is the first major attack against the coalition forces in several weeks.
It comes days after Israel reportedly responded to an Iranian attack with a drone strike on the Islamic republic, amid tensions fuelled by the Gaza war.
The statement from the Iraqi security forces accused "outlaw elements of having targetted a base of the international coalition with rockets in the heart of Syrian territory", at around 9:50 pm (1850 GMT).
The security forces burned the vehicle involved in the attack, the statement added.
Rami Abdel Rahman, director of the Syrian Observatory for Human Rights war monitor, said several rockets had been fired "from Iraqi territory at the Kharab al-Jir base" in northeast Syria, where US forces are stationed.
He accused the Islamic Resistance in Iraq, a loose alliance of Iran-backed groups, of staging the attack.
The group has claimed most of the attacks on US forces carried between mid-October and early February.
Following a series of rocket attacks and drone strikes by pro-Iran armed factions against US soldiers deployed in the Middle East over the winter, there had been several weeks of calm.
- Rising regional tension -
The Islamic Resistance in Iraq has said it is acting in solidarity with Palestinians and out of anger at US support for Israel in the Gaza war.
A January 28 drone attack killed three US soldiers in the Jordanian desert on the Syrian border.
In response, the US military struck dozens of targets in Syria and Iraq, aiming for pro-Iran forces, and drawing criticism from the governments of both countries.
The United States has around 2,500 soldiers stationed in Iraq and nearly 900 across the border in Syria as part of an international coalition created in 2014 to fight the Islamic State group (IS).
Sunday night's rocket attack came against the background of increasing tension in the region, with a flare-up between Iran and Israel.
Early on Saturday, an explosion at an Iraqi military base killed one person and wounded eight others.
Security forces said the blast hit the Kalsu military base in Babylon province south of Baghdad, where regular army, police and members of Iraq's Popular Mobilisation Forces, or Hashed al-Shaabi, are stationed.
CENTCOM, the US military command in the region, denied involvement in a strike there. The Israeli army refused to comment.
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