Air traffic control alerted the neighbourhood policing team based at the airport to the unmanned aircraft being flown in and around the airfield at around 1pm last Saturday.
The police helicopter was deployed to the area to assist officers on the ground who were searching the area to try to identify who was flying the drone.
Officials tracked the drone heading to the Eccup area and the helicopter was sent to search that area but was unable to find it.
Aircraft were grounded during the search but normal service was able to resume at the airport a short time later.
Inspector Andy Loftus, who heads the Outer North West neighbourhood policing team, said: "We are continuing to carry out enquiries in an effort to identify who was flying this drone, and we would like to hear from anyone with any information that could assist the investigation.
"These remote-controlled aircraft normally have a fairly limited range and battery life so it’s likely the person involved was somewhere in the wider area around the airport and we want to speak to anyone who thinks they may have seen them.
"Clearly the airport is controlled airspace and any unauthorised flying in that area presents obvious risks.
"We appreciate that radio-controlled drones are increasingly popular and we don’t want to detract from the pleasure people get from flying them but we hope this incident will help to serve as a warning to people of the potentially serious consequences of using them in areas where it is not safe."
A Leeds Bradford Airport spokesperson said: "We work closely with West Yorkshire Police and as such the incident on Saturday was concluded swiftly, with minimal disruption. We would like to reiterate that flying drones in the controlled airspace around LBA is prohibited."
Anyone with information is asked to contact the Outer North West team via 101 quoting log number 947 of June 3 or call the independent charity Crimestoppers anonymously on 0800 555 111.