The White House said the move ran contrary to the military's commitments to foster an "inclusive political process."
White House spokesman Josh Earnest said the arrest was the "latest in a series of actions that the Egyptian government has taken that does not reflect their commitment to an inclusive political process."
"It certainly is an act that is contrary to a legal system that is insulated from politics," he said.
Badie, who was arrested earlier today, is to be held for 15 days on allegations of having incited the murder of protesters, Egyptian state television reported.