The officials blamed the Taliban, who they said had accused the women of “moral deviation and adultery”.
The police said two men had been arrested in connection with the murder.
The attack was only 300m from the governor’s office in Ghazni city, which is on a list of places to be transferred to Afghan security control.
The incident happened on Thursday in the Khawaja Hakim area of Ghazni city, where the family lived.
The BBC’s Bilal Sarwary in Kabul says it is close to the governor’s office, the police chief’s office and a Western-backed Provincial Reconstruction Team.
Security officials said armed men entered the house where the young widow lived with her daughter, took them out, and stoned them to death.
“Neighbours did not help or inform the authorities on time,” an official said.
Officials said a number of religious leaders in the city had been issuing fatwas (Islamic religious edicts) asking people to report any one who was “involved in adultery”.
Ghazni has seen an upsurge in violence in recent years.
Strategically located on the route between Kabul and Kandahar, the province was once a centre of trade.
Ghazni city is on the list of areas to be transferred from Nato to Afghan control but critics say the government is struggling to secure it.