Reports say that 54 survivors have been taken to the hospital.
In all, eight crew and 192 or 193 passengers were on the plane, suggesting the death toll may rise by several dozen.
Many of the passengers of the plane were children flying from Moscow to a holiday came on the shores of Lake Baikal, the world's largest lake and a popular holiday destination.
Reports suggest the plane slid off the runway and burst into flames after breaking through a concrete wall and crashing into nearby buildings.
Only the plane's tail section was left intact.
Transport Minister Igor Levitin said the plane's pilots had told air traffic controllers they had landed successfully but then radio contact broke off suddenly.
Levitin said the runway was wet after rain, but the precise cause of the crash is unclear. Officials said the two flight recorders had been recovered and sent to Moscow for examination.
The airline carrier, Sibir, is Russia's second-largest.
The 220-seat jet, an Airbus A-310, was built in 1987 and had clocked up 52,000 flying hours in more than 10,000 flights.
Airbus says it is sending a team of experts to Russia to assist in the investigation.
The disaster is the fourth air crash in Irkutsk in the past 12 years.
In January 1994, a TU-154 aircraft crashed on takeoff, killing 124 people. In December 1997, an An-124 military transport aircraft crashed in a residential area of the city, killing 72 people.
Irkutsk airport was the scene of another fatal crash, in July 2001, when a TU-154 plane plunged to the ground as it was making its final approach to the runway. All 145 on board died.
This is the second Airbus crash in Russia in recent months.
In May, an Airbus A-320 belonging to the Armenian airline Armavia crashed in the Black Sea while trying to land at the Russian seaside resort of Sochi in bad weather. All 113 passengers and crew were killed.