BAA, which operates six UK airports, said the figures represent a growing confidence in business travel, because Heathrow is associated with commercial use.
The figures are in contrast to other UK airports, with Stansted suffering a 4.3% decline in September.
BAA chief executive Colin Matthews said: "The growth reflects an improved outlook for our airline customers and an increase in business confidence, as shown by cargo figures, which continue to outperform the pre-recession peak.
"Our £1bn a year investment programme continues, in order to offer our growing numbers of passengers a quicker, easier and more enjoyable travel experience."
Across all of BAA's UK airports, 9,988,178 passengers travelled during September, up 3.3 % (320,370) from 9,667,808 last year.
Edinburgh rose 2.2% to 873,195 while Southampton remained consistent rising to 174,570 from 174,501.
Glasgow's traffic declined by 5.7%, and Aberdeen by 5.1%, but BAA added that these falls are contracting as carriers fill the gaps in services left by the collapse of Flyglobespan.