A Boeing AH-64E Apache Guardian took flight from Thruxton, near Andover, at around 10.25am on Tuesday, April 28.
A real-time flight tracking service, FlightRadar24, reported the Army Air Corps aircraft to be circling around Monkton Up Wimborne and Sixpenny Handley before heading towards Salisbury.
A spokesperson for the British Army said the aircraft was likely carrying out a training exercise in the area.
The Boeing AH-64E Apache Guardian is said to be the most advanced and modern version of the aircraft used by the British Army.
The Ministry of Defence describes the aircraft to be designed to find and destroy air defence units, tanks and armoured vehicles.
The Apache can detect and classify up to 256 potential targets, display 128 of these to the crew and prioritise the top 16 threats.
It carries a mix of weapons including a 30mm chain gun, 70mm rockets and Hellfire missiles.
The aircraft is 4.72metres tall, has a main rotor diameter of 14.63metres and has a maximum weight of 7746kg.
It can reach a maximum speed of 330kph.