The figure is 5.8% up on the same month last year with new routes continuing to perform well and airlines flying bigger and fuller aircraft.
It follows another record month in August when 1,473,132 passengers passed through the terminal, an increase of 4.9% on last year and the second busiest month ever at the airport.
The busiest month on record was July 2018 when the 1.5 million passenger barrier was broken for the first time by a Scottish airport.
Airport CEO, Gordon Dewar, enthused: “It’s another impressive month for all of us at Edinburgh Airport and I must commend everyone who works at the airport for playing their part in our busiest ever summer as we welcomed more than 4.3 million people over the past three months.
“We have a fantastic range of destinations and airlines for passengers looking for that beach holiday or city break and we’re always looking to add more, such as this month’s fantastic addition in Dubai with Emirates.
“While this growth is helpful, we can’t escape the fact that Scotland is well below European average growth. We’re also seeing airlines announcing reductions and cuts to services due to us having the highest aviation tax in the world, something which is holding back the industry’s true potential.
"With the further challenge of an uncertain Brexit looming, the promised APD reduction needs to be delivered to avoid a stall in aviation and tourism growth.”