The Dutch ace has fractured metatarsal bones in his left foot and it's a major blow to the Premiership leaders.
Robben, 21, is reported to have told a Dutch newspaper: "Six weeks is the average time to heal this injury and then I need a few more weeks to be completely fit again.
"I had a feeling it was serious but because of the swelling it was impossible to make a final diagnosis."
But Chelsea are hopful Robben will be back some time next month.
Mike Banks, Chelsea physio, said: "The fractures are tiny and he could be playing next month.
"One is a chip on the side of his foot, the other is a small break on the third metatarsal.
"But this is not the traditional metatarsal that has become so famous since the last World Cup and which has kept Scott Parker out for two months."
Robben's injury occured during Chelsea's bruising Premiership victory at Blackburn Rovers last week.