Vivek Prakash/Reuters

MUMBAI—For over 30 hours following the death of the Shiv Sena leader Bal Thackeray on Saturday, stores throughout Mumbai closed their shutters and taxis and auto-rickshaws stayed off the streets. While analysts throughout Mumbai debated whether the citywide shutdown following the death of Mr. Thackeray was inspired by fear or respect, one 21-year-old woman and her friend were arrested for raising a similar question.

On Sunday, the police in Palghar, in Thane district, on the outskirts of Mumbai, arrested Shaheen Dhada after she posted a status update on Facebook that questioned the shutdown, also known as a bandh. A local daily, The Mumbai Mirror, reported that Ms. Dhada had written, “People like Thackeray are born and die daily and one should not observe a bandh for that.” The police also arrested her friend who “liked” the post, whom NDTV identified by her first name, Renu.

The women were arrested under Section 505 of the Indian Penal Code for “statements creating or promoting enmity, hatred or ill will between classes.” Srikant Pingle, in charge of the Palghar police, told India Ink that the local Shiv Sena chief, whom he identified as Mr. Bhushan, filed the complaint against Ms. Dhada because her comment on Facebook hurt Shiv Sena’s sentiments. Mr. Pingle declined to comment further on the details of the arrests.

Sudhir Gupta, the defense counsel for the two women, told NDTV: “Their posts don’t incite violence. It can’t be said they have made any derogatory remarks. They don’t belong to any political ideology.”

In a phone conversation with India Ink, a police officer of the Palghar station, who identified himself only as Gavali, said that the arrest took place on Sunday night and that the two women had been taken to court on Monday.

The two women, who were sentenced to 14 days in jail by the court, received bail after a bond of 15,000 rupees ($270) was paid, reported NDTV.

The Times of India reported that a mob of 2,000 Shiv Sena workers vandalized her uncle’s orthopedic clinic in Palghar. Repeated calls made to the Dhada orthopedic hospital in Thane went unanswered, while Harshal Pradhan, a Shiv Sena spokesman, said that he was unaware of the incident.

A police officer at the Palghar Police Station, who spoke on condition of anonymity, said that no one has been arrested in the attack on the clinic.

Pranesh Prakash, policy director with the Center for Internet and Society, said the arrests of the two women were a violation of free speech and the misapplication of the law. “There were thousands of people on Facebook, Twitter and in person who were saying the exact same kinds of things that this girl is alleged to have said,” said Mr. Prakash. “And the fact that only she and one other person who liked that comment have been arrested shows a clear arbitrariness in the application of the law.”

In an open letter addressed to the chief minister of Maharashtra, the former Supreme Court Judge Markandey Katju defended the two women, saying, “To my mind it is absurd to say that protesting against a bandh hurts religious sentiments.” He further said that the arrest appears to be a criminal act as it is a crime to wrongfully arrest or wrongfully confine someone who has committed no crime.

On social networking sites, people came out in support of Ms. Dhada and her friend. The Facebook group “Ban Shiv Sena” had about 36,400 “likes” as of Monday afternoon, while the party’s official Facebook page had just under 2,700. On Twitter, several commenters expressed solidarity with the two women, including Milind Deora, the government minister of state, communications and information technology, who said, “To learn who rules over you, simply find out who you are not allowed to criticize ~ Voltaire.”

In Maharashtra, Shiv Sena has a history of banning books, movies and other popular culture that are critical of the political party. In 2010, Rohinton Mistry’s book, “Such a Long Journey,” was withdrawn from the syllabus of Mumbai University after Shiv Sena officials complained that the book insulted Bal Thackeray. Ironically, in a January 2007 interview with Shekhar Gupta, the editor in chief of The Indian Express, Mr. Thackeray said that what differentiated him from the mafia is that journalists and others were free to disagree with him and criticize him.

Hari Kumar contributed reporting from New Delhi.