The Team Sky leader, who is now over 16 minutes adrift of Nibali, told his team's official website: "I have not been feeling 100 per cent so I went on antibiotics to try and knock the infection on the head.
MORE: Nibali grows lead as Majka grabs maiden Tour win
"I have been feeling it on my lungs and I haven't been breathing well.
"All the guys have been riding so strongly for me, but this bug has really taken it out of me. It's just one of those things unfortunately."
Porte was given the responsibility of team leader after the withdrawal of Chris Froome through injury.
Meanwhile, Vincenzo Nibali has denied that his prospective Tour de France win will be cheapened by the absences of Froome and Alberto Contador.
The Astana rider extended his lead over his rivals in stage 14 of the race on Saturday as he finished second behind Tinkoff-Saxo's Rafal Majka, who claimed his maiden stage win on the gruelling route from Grenoble to Risoul.
Nibali finished a minute ahead of closest rival Alejandro Valverde of Movistar, who is now four minutes and 37 seconds off the pace in the general classification.
Both defending champion Froome and two-time winner Contador have been forced to withdraw from this year's race after crashing on stages five and 10 respectively.
The 29-year-old Nibali has taken full advantage of the retirements of Froome and Contador with an excellent performance, and he was quick to reject talk that his title would mean less due to the demise of the pre-race favourites.
"Last year, I won virtually all the races I rode, where there were often also Alberto Contador and Chris Froome," he said.
"The only race I didn't ride was the Tour. This year, I've come to the Tour with great form and so I don't think anything is cheapened.
"I've had a great season in 2013, winning the Giro d'Italia and finishing second at the Vuelta, I don't think I'm any less of a rider than Contador and Froome."