The Britain-based Syrian Observatory for Human Rights monitor said 17 people, most of them children, were also injured in the shelling.
An AFP photographer saw the body of one child, a girl, lying on a bed at a makeshift hospital, her face bloodied and her clothes torn.
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At the kindergarten, smears of blood were left on the tiled floor, underneath a small red slide propped against a wall painted with children's drawings.
Harasta is in the rebel stronghold of Eastern Ghouta, outside Damascus, a region that is regularly targeted by government air strikes and shelling.
More than 300,000 people have been killed in Syria since the conflict began in March 2011 with anti-government protests