It would make an apology “if it was civilised enough”, Joseph Nkaissery said at a news conference.
The hashtag #SomeoneTellCNN is trending worldwide as Kenyans condemned CNN, which has not yet commented.
Its report focused on the threat posed by the al-Qaeda linked al-Shabab group.
Mr Obama was “not just heading to his father’s homeland, but to a region that’s a hotbed of terror”, said the CNN report.
With its headquarters in neighbouring Somalia, al-Shabab has carried out a spate of attacks in Kenya.
In the worst atrocity, 148 people were killed when it carried out a day-long assault on Garissa University College in April.
Mr Nkaissery said Kenya was at risk of attack like any other country, but this did not turn it into a “hotbed of terror”.
“I urge Kenyans to treat the @CNN report with the contempt it deserves,” he said, according to a tweet by Kenya’s privately owned Daily Nation newspaper.
CNN quoted security analyst Seth Jones analyst as saying that al-Shabab could carry out an attack during Mr Obama’s visit.
“Security for the president is likely to be very significant and that means what Al-Shabaab is likely to do, based on what it has done very recently, is go for a soft target,” he said.
On Wednesday, Kenya’s civil aviation authority said the East African state’s airspace would be shut for a 50-minute window ahead of Mr Obama’s arrival in the capital Nairobi.
A ban on planes flying lower than 20,000 feet will remain in place in Nairobi for the duration of Mr Obama’s three-day visit, it added.
The US issued a travel warning for Kenya in July ahead of the visit.