The incident took place around 6 p.m. in Mangolpuri area of west Delhi.
Birla, a minister in the Aam Aadmi Party government, said in a complaint to police that she had gone to attend a ceremony held in Mangolpuri's R block to welcome her.
"While returning from the ceremony, someone threw an object at my car causing a crack in the windscreen," Birla told police.
The 26-year-old Birla, a former journalist, is the youngest member in Chief Minister Arvind Kejriwal's cabinet. She holds the women and child development and languages portfolios and is also in charge of taking special measures for the safety of women.
A case has been registered, a police officer said.
"We were returning after attending a function organised near Santoshi Mata temple in Mangolpuri area," Birla's father Bhupender Singh, 55, told IANS.
"As soon as our car moved barely 50 metres, an object hit the front windscreen of the car and it was cracked. My daughter is unhurt. We did not see anyone throwing any object at the car, so we have no problem from the incident," Singh said.
Birla holds a Masters degree in journalism from the National Broadcasting Academy in Sarojini Nagar in south Delhi.
A Dalit, her mother is a sweeper at a government school where Birla studied till Class 12. She first joined Anna Hazare's anti-corruption movement and later joined Kejriwal's campaign.
--IANS (Posted on 05-01-2014)