The embassy school has also closed for the day and US citizens travelling in India, home to the world's third-biggest Muslim population, have been urged to exercise caution and monitor the local media for security updates.
Police in Muslim-majority Indian Kashmir fired tear gas at protesters on Friday who defied an unofficial curfew in the main city of Srinagar, where angry demonstrations are common after Friday prayers.
Kashmir was roiled by protests last Friday and police in the southern Indian city of Chennai detained 86 protesters who attacked the US consulate, smashing windows and security cameras.
By mid-afternoon on Friday, there were no reports of demonstrations in New Delhi or elsewhere in India.
Google has blocked access in India to the low-budget film "Innocence of Muslims" on video-sharing website YouTube. The Indian government has condemned it as "offensive".
Elsewhere in South Asia, a small group of Muslims held a demonstration in Sri Lanka and security was heightened in the diplomatic quarter of Dhaka in Bangladesh.
France also shut its cultural centres in Dhaka, fearing a backlash over cartoons of the prophet Mohammed published in a French satirical magazine.