According to reports, the missile exploded in mid-air, scattering debris over the farm, which is situated in the desert north of As-Sailiyah.
A Qatari military police vehicle was stationed at the entrance to the farm and reporters were refused access to the site, about 20km southwest of Doha, Qatar's capital.
Qatar, a member of the pro-Western Gulf Co-operation Council, hosts the US army's Central Command which directed the US-led invasion of Iraq in March 2003.
The Patriot is a surface-to-air missile system used by the US military and several of its allies, including Israel.
The US military has two bases in Qatar, As-Sailiyah and Al-Udeid. The latter is located in the desert further south of the capital.