The attack occurred in northern Kenyan town of Mandera at 3 a.m. local time, reported Xinhua, quoting regional police commander Charlton Mureithi.
"No arrest has been made but we hope to catch them soon. They caused huge destruction," he said.
According to police, the investigations have been launched to establish the motive of the attackers and arrest those who threw the grenades at the police station and escaped.
Earlier, a civilian was killed and four others were injured in Wajir town Wednesday evening after unidentified gunmen hurled two grenades at a crowd.
Meanwhile, the investigation into the attack Saturday at Westgate shopping mall in Nairobi that killed over 68 people is underway to establish the identities of the terrorists.
It is not clear whether the two attacks in Mandera and Wajir towns were related to the bloodbath in Nairobi, officials said.