Residents told the AFP news agency that three rockets struck near the villas where American oil experts from Safer live.
In a statement posted on an Islamist website, the Jund al-Yemen Brigades said it "launched five mortar shells at the American embassy in Sanaa".
The US-based SITE Intelligence Group, which monitors such websites, said the statement did not give a date for the attack but acknowledged that one shell missed the target and hit the neighbouring school.