Clay is the British No 1's least favourite surface and he never looked like getting the better of Clavet in a match delayed by rain.
Henman lost the opening four games of the first set and Clavet, who reached the last 16 at Wimbledon last year, took it easily 6-1.
Having taken time to settle, Henman found some form at the start of the second set and established a 4-2 lead. But a double fault in the next game enabled Clavet to break back, and the Spaniard, having regained the initiative, went on to wrap up a straight sets victory.
Injuries to the top two seeds - Pete Sampras and Carlos Moya - meant that Henman was the second highest seed remaining in the event, yet the Briton's preparations for the French Open had got off to a good start when he defeated Argentina's Mariano Puerta in three sets in the opening round.
In Tokyo, the former Wimbledon champion Richard Krajicek, of the Netherlands, was the biggest quarter-final casualty of the Japan Open when he was beaten by Sweden's Jonas Bjorkman.
The Dutch top seed failed to keep his momentum as he went down 6-3, 5- 7, 1-6. It was Bjorkman's second straight win over Krajicek - and the world No 32 will now take on the German Nicolas Kiefer, who defeated another Swede, Thomas Enqvist, 6-7, 7-5, 6-4.