Street, who is seeking re-election, quickly sought to reassure city residents that his office was not the subject of an investigation.
"I have done nothing wrong," Street said at a news conference.
FBI spokesman Linda Vizi said the device was not connected to any campaign espionage, but she refused to say whether Street was being investigated or whether the FBI planted the device.
Police said officers inspect the mayor's office every three or four months.
Tuesday's discovery comes near the end of a heated mayoral campaign that pits Street against Republican challenger Sam Katz for the second time. Street beat Katz four years ago by less than 10,000 votes in the city of 1.5 million, and polls show a neck-and-neck race again this year.
The Katz camp had nothing to do with the device, campaign spokeswoman Maureen Garrity said.
In August, someone tossed what might have been an unlit firebomb through the window of a Katz campaign office, and Katz has accused a Street supporter of brandishing a gun and telling Katz and his wife, "You're going down."
Supporters of Street, who is black, have accused Katz, who is white, of race baiting.
Street said he was confident the device was not placed by law enforcement.
"The question that ultimately will get raised in the minds of some people is who's investigating the mayor's office?" Street said. "Well, in response to that question, I want to assure the people of this city that this mayor is not being investigated. I have done nothing wrong."
By Eric Tucker