The helicopter swooped on Durdham Down at about 14:40 BST on Sunday, with air crew reporting the kite was soaring 1,000 feet (300m) up in the air.
No action was taken against the man, who was told the flying limit was 240 feet (73m).
The pilot said the kite endangered small aircraft from Bristol Airport.

It is thought to be the first such case since the plane went missing between Kuala Lumpur and Beijing in March 2014.
The children's mother said she had accepted compensation from Malaysia Airlines and the government so the boys could move on with their lives. The amount has not been disclosed.
The search for the plane, which was carrying 239 people, continues.
The family of Jee Jing Hang, who was on the plane, brought a lawsuit against Malaysia Airlines on behalf of his two young sons last October for breach of contract, as it had failed to deliver passengers to Beijing.
The family also brought claims against the Malaysian government, the Department of Civil Aviation, the immigration department and the air force for negligence.
"The court was informed that all the parties in the suit had come to an amicable settlement," Gary Edward Chong, a lawyer for the family, told the AFP news agency on Tuesday.
The families of other victims have been following the case closely and experts believe this settlement will trigger other similar legal actions.
No wreckage from the flight has ever been found and an Australian-led team is still scouring the southern Indian Ocean seabed in hope of finding the aircraft.
Four months after MH370 vanished, another Malaysia Airlines plane - flight MH17 - was shot down by a suspected ground-to-air missile while in Ukrainian airspace, with the loss of 298 passengers and crew.
The airline was declared "technically bankrupt" by its chief executive on Monday as he announced plans to cut about 6,000 jobs.

The justices voted 5-4 to grant an emergency appeal from the clinics after a federal appeals court had earlier upheld the new Texas law.
Clinics have argued that the measures will lead to a second major wave of Texas clinic closures in as many years.
The southern US state had 41 abortion clinics in 2012 but only 19 remain.
The new restrictions were due to take effect on 1 July.
They require abortion clinics to meet hospital-grade standards and for doctors at the clinics to have admitting privileges at a local hospital.
Critics say both provisions are designed to shut down abortion providers and will force women to seek abortions at illegal and unlicensed facilities.
Monday's ruling means clinics unable to meet the restrictions will remain open at least until the Supreme Court decides whether it will hear the appeal from clinics.
A police helicopter landed on an area of Bristol parkland to order a high-flying kite enthusiast to bring down his craft.
[NEXT_CONCEPT]
Two Malaysian children who lost their father on flight MH370 have settled their negligence case out of court.
[NEXT_CONCEPT]
Several abortion clinics in Texas will remain open after the US Supreme Court decided to put strict new measures against them on hold.