The president had given the security forces a week to catch Nshimirimana’s killers.
The prosecutor said a military vehicle had been used by the killers and subsequently burned.
The vehicle had been identified and came from a military camp in the centre of the capital Bujumbura, it added.
According to witnesses quoted in the local media, the attackers were wearing military uniforms.
Nkurunziza’s candidacy was condemned as unconstitutional by the opposition and provoked months of protests.
In mid-May, rebel generals attempted a coup. They have since launched a rebellion in the north of the country, close to the border with Rwanda.