Russian officials say the blast occurred around 8:30 a.m. local time as Yevkurov was traveling near the regional capital Nazran.
He was hospitalized, and Federal Emergency Situations Ministry officials said he was in critical condition.
At least three other people were wounded in the attack, Russian news agencies reported.
ITAR-Tass said three bodyguards were killed.
Yevkurov is the third top official to be wounded or killed in Ingushetia in the past three weeks.
compiled from agency reports, June 22, 2009, rferl.org