Federer then won his next service game without dropping a point to lead 5-2.
Henman then had to take a break to receive a neck massage and, after Federer broke serve again, he called it a day.
Rain then came down, interrupting the match between Lleyton Hewitt and James Blake before play was abandoned for the day.
The Australian No 1 seed was leading 6-4, 3-1 against the young American when the downpour started.
Earlier American Andre Agassi had beaten eighth-seeded Swede Thomas Johansson 7-5, 6-2 to reach the quarter-finals. Agassi's next opponent will be Nicolas Lapentti, of Ecuador, who beat Adrian Voinea, of Romania, 6-2, 3-6, 6-3.
In the women's event Venus Williams, of the United States, seeking her fourth title in the tournament, became the first semifinalist by fighting back to beat Elena Dementieva, of Russia, 5-7, 6-3, 6-2.
Williams overcame 48 unforced errors and 10 double faults to extend her winning streak in the championship to 22 matches.