Many Muslims visit the graves of deceased relatives during Eid as part of traditional celebrations after the holy month of fasting.
Police were unable to confirm the cause of the explosion in the Ghani Khel district of the province of Nangarhar.
"An explosion happened in a graveyard," Hazrat Hussain Mashriqiwal, police spokesman for Nangarhar, told AFP.
"Ten women were killed in the blast, two other women and a child were also wounded."
President Hamid Karzai delivered an Eid address that again urged the Taliban to halt 12 years of war as the country seeks stability before next year's elections and the withdrawal of NATO-led troops.
In a thinly-veiled reference to neighbouring Pakistan, Karzai appealed to the Taliban to resist being controlled by foreigners and said the militants should support their own country.
"You are working for others, (foreign) guns are put on your shoulders, and innocent Afghan people are being killed by it, homes are destroyed," he said.
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