The directive came after reports that Kashmiri students were verbally abused and beaten in the northern Indian state of Rajasthan.
Kashmir saw fresh clashes between troops and protesters amid attempts to hold a by-election earlier in April.
Mr Singh said that Kashmiris were part of India's "family".
Muslim-majority Kashmir is at the centre of a decades-old territorial dispute between India and Pakistan.
Both countries claim Kashmir in its entirety and control different parts of it. India accuses Pakistan of supporting separatist sentiment in Kashmir, but Islamabad denies this.
In a tweet, Mr Singh said: "The Kashmiri youth also contribute in the progress of India. Action should be taken by the states against those who target them".
His comments came a day after six Kashmiri men studying at a university in Rajasthan were allegedly called terrorists and beaten up by locals.
Billboards that refer to "stone-pelting Kashmiris" and ask them to leave have also appeared in the northern state of Uttar Pradesh.
The latest bout of violence in Kashmir has killed nine people. Local protesters have been hurling stones at security forces who have been accused of opening fire into the crowds.
A viral video of a group of Kashmiris heckling a soldier has also contributed to anti-Kashmiri sentiment in the rest of the country.
There has been an armed revolt in the Muslim-majority region against rule by India since 1989.
High unemployment and complaints of heavy-handed tactics by security forces battling street protesters and fighting insurgents have aggravated the problem.
India's Home Affairs Minister Rajnath Singh has told state governments to ensure the safety of students from Indian-administered Kashmir.