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.
BBC Somali service reporter Abdullahi Abdi says al-Shabab appears to be firmly establishing itself in Garissa County, despite government efforts to defeat the militants.
The policemen were ambushed while rushing to the aid of colleagues who had been hit by a landmine explosion, he says.
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.
Analysis: Abdullahi Abdi, BBC Somali service
There have been reports of al-Shabab fighters roaming between villages in north-eastern Kenya for the last three weeks.
Local reports have spoken of groups of 20 to 40 militants in different areas, armed with sophisticated weapons like hand-held rocket launchers, walkie-talkies and vision cameras.
Last week, they occupied Yumbis for a whole day, despite the heavy presence of police and soldiers in the region.
Garissa County Deputy Commissioner Ahmed Adan Shabeel says the thick forest in the area, and the fact that al-Shabab fighters include local residents who know the terrain better than soldiers, makes it difficult to drive them out.