There was further bad news for Henman when Argentine fourth seed David Nalbandian staged a remarkable quarter-final comeback to beat German sixth seed Rainer Schuettler 4-6, 7-6 (7-5), 6-3.
Nalbandian, who had trailed by a set and a break, needed the win to keep alive his slim chances of overtaking Henman in the race for next month's lucrative Masters Cup finale.
Henman, though, can make sure of a place in the eight-strong Masters Cup field by reaching the quarter-finals at next week's Paris Masters.
"It's a bit soon to think about my feelings for Paris but it's going to be an important week for sure," Henman said.
"Of course it's disappointing to go out here in Basel, but I'll be coming away with a lot more positive aspects than I did after (last week's Masters Series tournament in) Madrid.
"I feel like I'm hitting the ball well again now, and playing well, and the fact that I'm defending the title in Paris will also give me confidence."
Certainly there was little to separate Henman and Novak, but a few stray shots from the Briton coupled with greater Novak efficiency on the break points were enough to see the Czech through.
Novak, who also ended Henman's medal hopes in the first round of the Athens Olympics, will now face Austrian world number 73 Stefan Koubek in the Basel semi-finals.
Koubek fought back from a set down on Friday to beat Croatia's Ivan Ljubicic 2-6, 7-5, 7-5, a win which earned the 27-year-old from Klagenfurt his first ATP semi-final place this year.
Saturday's second semi-final will pit Nalbandian against double Olympic gold medallist Nicolas Massu.
The 25-year-old Chilean beat Czech Bohdan Ulihrach 6-2, 7-6 (7-4) on Friday to register his best tour result since Athens.
"After Athens it was difficult for me to concentrate on my career because in Chile my Olympic win was so big," Massu said after stepping off court.
"But I'm feeling good again now and if I can win my semi-final, I think I can win the title."
