Elizabeth Mulinge was leading the Utawala interdenominational church in prayers when the attack took place, the woman's daughter, Beth Mwathi, told state-run Kenya Broadcasting Corp.
"My mother was leading the prayer session when I heard a loud bang, we were forced to lie down, after a few seconds we woke up only to find some of the worshippers bleeding profusely and writhing in pain including my mother," Mwathi said.
The church is situated inside an anti-shifta -- or anti-rebel -- administration police camp. The officer who died served as the pastor of the church.
Garissa police head George Losku said officers are searching for the attackers, adding that a suspicious vehicle was seen outside the church minutes before the blast.
"It is very early to say the attack was executed by al-Shabaab militants, however we cannot rule out their involvement. We are appealing to members of the public to give us information that could lead to the arrest of the assailants behind these spontaneous attacks that have rocked Garissa town,"he said.