The driver, Akhmed Nalgiyev, is a resident of Surkhakhi, a small town 10 kilometers east of the Ingushetian capital, Magas.
Nalgiyev was attempting to return home by car when he was stopped outside town by police and bodyguards for Yevkurov.
The authorities explained that Surkhakhi's streets were blocked off for the president's motorcade. Nalgiyev would have to wait to get back home.
Nalgiyev was apparently not in the mood to linger.
According to townspeople directly familiar with the matter, Nalgiyev stepped outside of his vehicle and entered into a short altercation with one of Yevkurov's most trusted bodyguards, Sulanbek Shadiyev.
Nalgiyev then brandished a firearm and shot the 36-year-old Shadiyev in the leg. Police returned fire, hitting Nalgiyev in the leg. Both men have been hospitalized, and neither is in critical condition.
Nalgiyev, currently under arrest, is expected to be charged with shooting a police officer on duty.
'Widespread Local Annoyance' At President's Visit
Yevkurov was in Sukhakhi to celebrate the 200th birthday of Batal Khadzhi (Haji) Belhroev, a Sufi sheikh and native son whose followers were a longtime source of Muslim anti-Soviet resistance in the Caucasus.
According to sources in Surkhakhi, there was widespread local annoyance at the inconvenience associated with Yevkurov's visit.
In contradiction with sources on the ground, the president's press secretary has denied that any members of Yevkurov's entourage were hurt in the shooting, saying that Nalgiyev shot a local police officer.
In June 2009, Yevkurov survived a major assassination attempt when a suicide bomber attacked the Ingush president's car, killing his driver and seriously wounding Yevkurov.
-- Charles Dameron, with reporting from Amina Umarova and Akhmed Sultanov