The fragmentation mine was placed on a parked bicycle in the district of Batticaloa and targeted the Special Task Force police commandos, the ministry said.
Fighting meanwhile continued across the northern territories of Jaffna, Vavuniya, Mannar and Weli Oya, with security forces reporting they killed 15 Tamil Tiger rebels for the loss of two soldiers on Saturday, the ministry said.
There was no immediate comment from separatist Tiger rebels.
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Two days of clashes raises the number of rebels killed by security forces to 4,354 while 403 government troops have died in combat since January, according defence ministry figures.
Casualty claims cannot be verified as the military prevents journalists from travelling to rebel-held areas.
Fighting has worsened since Colombo pulled out of a six-year truce with the Tigers in January.
Tens of thousands have died since the Tamil Tigers launched their campaign to carve out a separate homeland for minority Tamils from the majority Sinhalese