War of attrition
Svetlana Gorbakova, a spokeswoman for Nazran's investigative committee, said that there had been "between three and five blasts".
She said the city's police chief and the head of its investigative committee were among the injured.
Russian security forces are locked in a war of attrition with Muslim fighters throughout the North Caucasus, Russia's most volatile region, which comprises Chechnya and other mainly-Muslim republics.
The area is beset by nearly daily attacks which mostly target law enforcement and government officials.
An upsurge in violence in Ingushetia, Chechnya and neighbouring Dagestan in recent months has alarmed the Kremlin, nearly a decade after government forces defeated Chechen separatists in the second of two devastating wars.
Dmitry Medvedev, the Russian president, has described the instability and poverty in the region as the country's most serious domestic problem.
Local leaders in Ingushetia, which has a population of around 300,000, have said poverty and unemployment are fuelling the unrest.
But Russian officials often blame the violence on groups of armed men, many driven by Islamist ideology, who they say have tried to overthrow Moscow's rule since 2002.