The al-Shabab militants had ambushed the police near Yumbis town in Garissa County, Mwenda Njoka added.
He dismissed as propaganda al-Shabab’s claim that at least 20 policemen were killed in the attack.
Al-Shabab is a Somalia-based group which has stepped up attacks in Kenya.
In April, it carried out a siege on Garissa University College and 148 people were killed.
Last week, the militants briefly seized control of Yumbis, about 100km (62 miles) east of Garissa town, and warned residents not to work with the government.
Four police vehicles were set ablaze by the militants, he adds.
Al-Shabab said in a statement that its “special forces” had carried out a “successful” operation which led to the killing of at least 20 policemen.
However, Mr Njoka, the interior ministry spokesman, said only one officer was wounded and had been airlifted to hospital for treatment.