Leopold Koenig (Team NetApp) claimed victory on the 189.8-kilometre route from Welshpool to Caerphilly while Tiernan-Locke (Endura Racing) finished second to assume the race leader's gold jersey with two days of racing to go.
Named in the British team for next week's road World Championships, the 27-year-old from Plymouth, pictured above, whom speculation suggests will join Team Sky next year, began the day in sixth place, 24 seconds behind leader Leigh Howard (Orica-GreenEdge). But Tiernan-Locke, who received a six-second time bonus for placing second, now has a 13-second lead over Howard ahead of today's seventh stage from Barnstaple to Dartmouth. The eight-stage race concludes with tomorrow's Surrey route from Reigate to Guildford.
Wiggins was a non-starter in Welshpool after an eventful fifth stage to Stoke-on-Trent for Team Sky, in which Mark Cavendish relinquished the race lead to Howard.
"I'm sorry to have to pull out," said the Tour de France winner. "I've loved the last six days, meeting so many people around the country and enjoying seeing the crowds along the roads.
"It's been a great experience, but this bug sadly means I'll now miss the climax this weekend. I'm sorry I can't continue and would like to thank all those fans, of all ages, for the support. They have really inspired us this week and this summer."
Six riders formed the breakaway on a stage that included crossing the Brecon Beacons.
Their advantage was cut to less than a minute, with two ascents of Caerphilly Mountain preceding the finish in front of Caerphilly Castle.
On the first climb of the mountain, Tiernan-Locke attacked from the peloton as the escape group splintered in front of him. Only escapee Graham Briggs (Raleigh-GAC) could stay with him, but Koenig (Team NetApp) bridged the gap before Briggs fell back on the lower slopes of the second ascent of the finishing climb.
British academy rider Josh Edmondson was alone in pursuit but was swept up by a larger chase group, led by Ivan Basso (Liquigas-Cannondale), in the closing kilometres.
Koenig belatedly helped to share the workload with Tiernan-Locke in the closing moments before sprinting away to win by one second.
Nathan Haas (Garmin-Sharp) won the sprint for third to move to third place overall, 18 seconds behind.