The rocket, a Katyusha, did not explode, according to reports.
It adds to 24 hours of tension in Iraq that coincided with American Independence Day. There were claims the US had deployed a C-RAM system to confront threats to its embassy and other facilities.
The incident took place after a number of rocket attacks near the US Embassy in Baghdad and other US military sites in recent weeks.
A raid by Iraq security forces on some of their own members on Thursday night resulted in hours of uncertainty in Baghdad.
The US has carried out airstrikes on Kataib Hezbollah after it carried out rocket attacks on bases where US forces are located.
Iraqi corruption, lack of foresight contribute to its economic woes, analyst says
There was no immediate claim of responsibility.
Al Arabiya reported Wednesday night that sites belonging to the Popular Mobilization Forces were being shelled in eastern Syria, near the border with Iraq.
The US is the leader of the anti-ISIS coalition, has been training Iraq and has spent hundreds of millions to help Baghdad defeat ISIS.
The cleric has urged his unarmed supporters known as "blue hats" to work with authorities to ensure schools and businesses can operate normally again.