Eight other children were injured and being treated at a hospital, senior police official Faisal Kamran said, adding that the owner of the tutoring centre and another person had been arrested.
Kamran said rescuers were searching through the rubble after receiving reports that more children could be trapped beneath the debris.
He said the tutoring centre was housed in an ageing building and the roof of an unfinished second floor apparently collapsed on Tuesday because of poor construction quality.
Building collapses are common in Pakistan, where construction standards are often poorly enforced.
Many structures are built with substandard materials, and safety regulations are frequently ignored to reduce costs.
Witnesses said ambulances and rescue workers rushed to the scene after the roof collapsed.
Residents also joined the search, using shovels and their bare hands to remove rubble in an effort to reach children trapped beneath the debris.
Hours later, as the bodies of the children were being handed over to their families, scenes of anguish unfolded outside hospitals and in the neighbourhood on the outskirts of Lahore where the private tutoring centre was located in a house.
Parents wept over the loss of their children, while mothers and other female relatives cried and beat their chests in grief.
Most of the victims lived nearby, and funeral prayers were expected later on Tuesday.
Grief was mixed with anger as residents demanded stern punishment for the owner of the tutoring centre, blaming him for operating classes in what they described as an ageing and unsafe building.
Pakistan's President Asif Ali Zardari and Prime Minister Shehbaz Sharif expressed grief over the collapse of the roof of an evening school building in Lahore.
In separate statements, they offered condolences to the families of the victims, prayed for the speedy recovery of those injured, and said effective safety measures were needed to prevent similar tragedies.
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