Here are the latest developments:
The Sena has called the bandh to protest against the suspension of two policemen who arrested the young girls.
Because of the Sena's bandh, schools, colleges and markets are closed. Bus services are limited. The courts are working, but not many people have turned up there.
There is heavy police presence all around. At least 500 police officers and the Rapid Action Force have been posted to maintain peace. "People have joined the bandh on their own. The entire talka is shut. Business establishments are closed," said Shiv Sena leader Prabhakar Raul.
On November 18, as Mr Thackeray was cremated, lakhs of supporters filled the streets to follow the hearse's journey to the large Shivaji Park in Mumbai. Nervous about potential violence by the Sena, the city was quiet, choosing to stay indoors.
Shaheen Dadha, a young girl, questioned this on Facebook. Her friend Renu Srinivasan indicated that she liked her comment.
The next day, they were arrested, provoking public outrage.
Their arrest was based on a police complaint by Sena leader Bhushan Sankhe in Palghar, a strong base of the party.
The charges against the two girls have still not been dropped - they have been accused of deliberate and malicious acts intended to outrage religious feelings, making statements promoting enmity between classes and under the Information Technology Act.
The girls were released on bail within a few hours of their arrest. Sena workers vandalised a hospital owned by the family of one of the girls involved.
The Shiv Sena says the policemen who arrested the girls are being unfairly penalised and that they were acting "as per the situation".