A woman friend who “liked” the comment was also arrested, they said.
The women, accused of “hurting religious sentiments”, were released on bail after appearing in court in the town of Palghar, police told the BBC.
The death of the controversial Hindu nationalist politician on Saturday afternoon brought Mumbai to a halt.
Thackeray, one of the most divisive figures in Indian politics, was blamed for inciting tensions between Hindus and Muslims and was revered by his followers.
News of his death saw businesses shutting and taxis staying off the roads amid fears of violence by supporters of the right-wing Shiv Sena party he founded.
While his supporters grieved, many others were angered by the inconvenience to commuters and several people were critical on social media sites.
In her Facebook comment, the 21-year-old wrote, “People like Thackeray are born and die daily and one should not observe a ‘bandh’ (shutdown) for that.”
In recent months, police have arrested a number of people in cases which are being seen as a test of India’s commitment to freedom of speech.
In October, Ravi Srinivasan, a 46-year-old businessman in the southern Indian city of Pondicherry, was arrested for a tweet criticising Karti Chidambaram, son of Indian Finance Minister P. Chidambaram. He was later released on bail.
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