Henman, in his first quarter final since this year's Wimbledon, was beaten 5-7, 6-3, 6-4 by the top seeded Russian, though his performance in defeat suggested he is beginning to return to his form of six weeks ago.
The British No 1 got his tactics right, getting to the net at almost every opportunity, sometimes taking risks to do so, and trying to hustle Kafelnikov out of his rhythm on his dangerously consistent ground strokes.
"Kafelnikov is very solid from the back and I wanted to take the game to him as much as possible," Henman said. "The best players take their chances and there were some there I might have taken," Henman said.
"But I feel my performance put me back where I should be. However I don't want to do it for one week. I want to do it for the US Open."
At the RCA Championships in Indianapolis, the world No 1, Pete Sampras, suffered a surprise third-round defeat to Magnus Larsson, losing 7-6, 4-6, 7-6.
Andre Agassi saved three set points before beating the third seed, Alex Corretja of Spain, 7-6, 6-1.