Many countries have been taking precautions
He said the letter had been sent to an ordinary Kenyan citizen, and that four people had been exposed to the spores.
And in New York, a fifth case of infection was found on Thursday - when an employee at CBS television was diagnosed with skin anthrax.
The US House of Representatives in Washington has been shut down until at least Monday after a letter contaminated with anthrax spores was sent to the office of Senate Majority Leader Tom Daschle.
Atlanta postmark
Mr Ongeri said that the anthrax letter found in Nairobi had been posted in the US city of Atlanta on 8 September, and routed via Miami.
The letter was received in Nairobi on 9 October and opened on 11 October.
Mr Ongeri said that the people exposed to the letter were "not in danger".
Two other suspect letters are also being tested for anthrax, including one received by the United Nations Environment Programme in Nairobi on Wednesday.
That letter was posted in Pakistan, while the third letter, addressed to a businessman in the town of Nyeri, appeared to have been posted in Nairobi.
Mr Ongeri said Kenyans should not panic about the discovery.
"The government has the capacity and capability to deal with the situation," he said.
US concerns
Concern about anthrax has been increasing worldwide, with five people now infected with the disease in the United States, one fatally.
In Florida one man has died and another is receiving treatment for respiratory anthrax.
US law enforcement officials have said there is no evidence linking the anthrax scares with foreign terrorists.
But a note inside the letter sent to Mr Daschle warned: "You've been exposed to anthrax. You're going to die."
Tests have determined that the anthrax found in the letter was professionally made but was not weapons-grade.
Mounting concern about the US cases has triggered alerts and hoaxes around the world, with the Israeli parliament evacuated along with public buildings in Europe, Africa and New Zealand.