The activists shouted slogans like "Aamir Khan murdabad", "Aamir Khan chale jao", and attempted to force their way inside the actor's home in Bandra but were prevented by a substantial police presence there.
Later, around a dozen activists were detained and taken to the Bandra police station.
An official said police have deployed in adequate numbers to prevent any untoward incident.
On the issue of beefing up security, the official said that would be decided by a separate department depending on the requirement.
Meanwhile, while on a visit to Solapur, Maharashtra Chief Minister Devendra Fadnavis declined to comment on Aamir Khan's comment.
"I have better things to do than react to all such statements. There are more pressing issues of the state than talking about these things," Fadnavis told media persons.
In Pune, state Environment Minister Ramdas Kadam termed Aamir Khan's comments as "treason" and said the actor was welcome to go to Pakistan if he felt so insecure in India.
"In India, we gave you so much love -- Aamir Khan, Shah Rukh Khan and Salman Khan. We looked at your art and not your religion. Does it mean we have been feeding milk to a snake?" Kadam said.
In Satara, Nationalist Congress Party president Sharad Pawar on Tuesday declined to react to Aamir Khan's remarks while offering condolences to the family of Col. Santosh Mahadik of the Indian Army who died fighting militants in Jammu and Kashmir.