The British number one was competing in just her fourth match since reaching the last four at Wimbledon, but second seed Halep prevailed by a 6-4 7-6 scoreline.
Both players struggled on serve during the opening set, but Halep was more efficient when break-point opportunities came her way and the Romanian struck three times to move closer to the next stage.
It was a similar story in the second as both players shared four breaks of serve, but Konta was required to save match points before taking the set into a tie-break.
However, Halep stormed through it with minimal fuss and she took it by a 7-1 scoreline to progress in just under one hour and 50 minutes.
Konta will now turn her attention to the US Open, which begins on the final weekend of August.