The alternative rock trio were halfway through their set at the Summersonic Festival in Japan when Molko fainted.
He was taken off the stage and rushed to hospital where he made a full recovery.
The band later released a statement explaining Molko's collapse.
It read: "We have undertaken a gruelling and intensive schedule over the last few months and the last couple of weeks alone played 5 countries in 9 days.
"Brian picked up a virus which coupled with jet lag and exhaustion caused his collapse on stage. Thanks to prompt and professional care Brian is recovering well."
Molko isn't the first singer to fall ill while performing recently.
JET frontman Nic Cester collapsed during a concert at London's Hard Rock CafÃ© on Monday night (10.08.09).
He quickly stood up, joking he had swine flu before fainting again.
Nic was rushed to University College Hospital in Euston, where he was treated for symptoms of gastroenteritis, acute vomiting and dehydration and held overnight for monitoring.