The four-meter-high metal statue in the south Russian city, of two young men and a young woman mourning those who died in the battle, had already been weakened by corrosion, a local emergencies official told RIA Novosti.
The official said the male figures collapsed on Sunday evening, but the female remains standing.
The statue was built in 1973 on the 30th anniversary of the 200-day Battle of Stalingrad, the bloodiest battle in modern history. The city was renamed in Volgograd in 1961 after the death of Josef Stalin.
Last week, Russian media reported that Volgograd's best-known landmark, the colossal Motherland Calls monument, was in danger of a catastrophic end to its more than four-decade-long existence.
Specialists said the 85-meter-high statue, portraying a heroic sword-wielding woman and commemorating the Battle of Stalingrad, was in urgent need of repairs to prevent it from crumbling.
The battle, which raged from July 1942 to February 1943, eventually saw Soviet troops turn back advancing German forces, inflicting the first major defeat on Hitler's armies.
Combined military deaths alone during the battle are estimated at around 1.5 million, and the city was almost entirely razed to the ground. Some 40,000 civilians also died as the battle raged.
