Birla's car was "attacked" around 6 p.m. Sunday in Mangolpuri area of west Delhi when she was returning after attending a ceremony.
Speaking on the issue, Delhi Chief Minister Arvind Kejriwal said if any child had done anything, the matter is finished.
"If a child had done anything ... then all right. The matter is finished," said Kejriwal.
He also said he himself talked to Birla on the issue and she informed him that no child approached her to apologise.
"Birla called several party leaders saying that someone threw something on her windscreen and it cracked. She also asked the leaders if she should lodge a police complaint. She went to file the complaint after everyone told her to do so, as it was not clear who had done this thing," said Kejriwal.
A police officer said they were probing the incident and till now have found involvement of a child whose ball hit the car's windscreen when he was playing.
The police, according to sources, are now planning to submit the closure report in the case after recording the statement of the child before a non-governmental organisation.
Birla, 26 and a former journalist, is the youngest member in 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 regarding the incident was registered by police Sunday.
--IANS (Posted on 07-01-2014)