The attack comes just one week before the anniversary of the Beslan school siege.
A spokesman for Ingushetia's emergencies service said local Prime Minister Ibrahim Malsagov's car had been damaged by a bomb blast in the centre of the town of Nazran on Thursday.
He said Malsagov, 44, and three other people were taken to hospital, where the prime minister's security guard died.
Russian news agencies said Malsagov's wounds were not life-threatening.
Interfax news agency quoted a senior police official as saying there had also been an earlier, smaller explosion intended to divert the security forces' attention.
Police gave no indication as to who might have been behind the blasts, the second such incident in four days.
On Monday, one person was killed and another two injured when a bomb went off near Nazran's main hospital.
Security forces stormed the
school in Beslan to free hostages
Monday's blast was officially described as an act of "terrorism", the usual reference to separatist fighters from Chechnya and their local allies.
Moscow has been battling Chechen separatists for 10 years, and the violence frequently spills over into neighbouring regions. Nazran was briefly seized by Chechen rebels.
On 1 September 2004, Chechen rebels took more than 1000 people hostage in a school in Beslan, Northern Ossetia, which also neighbours Chechnya.
Three days later, more than 330 people, half of them children, were killed when security forces launched a messy storming of the school.