Three people reported started shooting inside and outside the terminal building before blowing themselves up when police opened fire, the BBC reported.
The Turkish prime minister has said early signs point to Islamic State as being behind the atrocity.
Flights were cancelled in the aftermath but many have since resumed, however there are significant delays and many cancellations.
The Independent has reported that British Airways has cancelled its flights today between Heathrow and Istanbul and its first outbound service from the Turkish city.
“We are keeping the situation regarding other scheduled flights to Istanbul under regular review and are awaiting more information from the authorities in Turkey,” the airline said.
The Foreign Office has noted the attack but its travel advice remains unchanged.
The Intrepid Group has decided to cancel all trips departing for Turkey until July 5 following the attack. It also confirmed that that none of its passengers were affected and are all accounted for.
"Our team of local experts is currently working on the ground in Istanbul to update us regularly on the security situation, and we are doing everything we can to provide support and assist with alternative arrangements for effected passengers," the company said.