A spontaneous shutdown saw businesses close across Srinagar, the region's major city, with protesters calling for retribution against "disrespect" to the prophet.
And in Indonesia, the world's largest Muslim-majority country, about 50 protesters staged a rally in front of the Indian embassy in Jakarta.
"The Indian government must apologise to Muslims and they must take strict action against the politicians who made the remarks," protest coordinator Ali Hasan told AFP.