The Iraqi satellite television channel Afaq TV, citing a report published by Arabic-language Ababeel news agency, said the diplomatic mission sounded sirens following the blasts, which occurred early on Thursday.
Ababeel reported that the explosions rocked the areas adjacent to the premises of the embassy.
No official statement has confirmed the report and no further details have been released.
On May 19, two Iraqi security sources, speaking on condition of anonymity, said an explosion had been heard in Baghdad’s Green Zone.
A source told Arabic-language Shafaaq news agency that the explosion was believed to have been caused by a Katyusha rocket slamming into the area.
The Green Zone is one of the world's most high-security institutional quarters. Located in the center of the Iraqi capital, it houses parliament, the prime minister's office, the presidency, other key institutions, top officials' homes and embassies.
The American embassy in Baghdad -- the world's largest -- lies within the fortified neighborhood, also known as the International Zone, which is surrounded by concrete walls.
Source: Press TV