The accused duo, identified as Murgesh Devendra alias Anna (45) and his aide Jibishar Rabba (19), were arrested from a hamlet named Baneli near Ambivali, senior inspector of Sion police station Yesudas Gorde said.
A motorcycle, a country-made pistol and a gold chain were recovered from them.
According to police, Anna has eight different criminal cases registered against him across various police stations in the city.
"From last week, sleuths of Sion police station were on his trail, as the latter had recently snatched a gold chain of a woman in the fish market area in Sion," Gorde said.
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"Anna used to steal motorcycles, change their number plates and then commit crimes of chain snatching," the senior officer said.
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Slamming the "overreaction" by authorities, human rights advocacy organisation Amnesty International India demanded the immediate release of the two men arrested for allegedly sharing the RSS chief's morphed image.
"Arresting people simply because they mocked public figures is an absurd overreaction by the authorities," said Abhirr VP, Campaigner at Amnesty International India, in London.