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Mass panic erupted after the hydrogen balloons exploded into a huge fireball, thought to have been caused by a smoker who lit a cigarette nearby.
More than 100 of those injured were taken to hospital with burns following the rally, staged two days before the election by the ruling Republican Party in the centre of the city.
One witness, a 30-year-old woman who identified herself as 'Susan', said: "I heard an explosion and saw flames rising high.
"People rushed away from the square, and I saw a man with a burnt face and a girl whose back was on fire."
A video posted online by internet television station Panorama.am showed a large but short-lived flame billowing in the middle of the crowd where hundred of white balloons had been flying moments before.
Health Minister Harutyun Kushkyan told state television many people were injured in the chaos as people tried to flee.
She described the condition of the injured as "satisfactory".
Opinion polls have shown the Republican Party and its coalition ally, Prosperous Armenia, winning more than 60 percent of the votes in Sunday's parliamentary election, signalling little or no change in government.
The 2008 presidential elections in Armenia - a landlocked ex-Soviet republic of 3.2 million that is Russia's main ally in the South Caucasus - were marred by violent clashes between opposition protesters and police.
There's only one pertinent question ask here. Who's the idiot that filled all those party balloons with hydrogen instead of helium?