Thousands of people, including tourists and Hindu pilgrims, are leaving Indian-administered Kashmir after local officials issued a security alert, the BBC reported.
Indian authorities warned of a "terror threat" against Hindu pilgrims heading to the Amarnath shrine.
Militants backed by Pakistan were planning an attack on the annual pilgrimage, officials have said.
India accuses Pakistan of backing militant groups based in Kashmir, something denied by Pakistan.
The 45-day pilgrimage began on 1 July and about 300,000 pilgrims have visited the cave shrine, located high in the Himalayan mountains, according to AP news agency.
Kashmir's government has advised them to leave the area "immediately", causing panic as visitors scramble to organise transport.
round 20,000 Hindu pilgrims and Indian tourists, as well as more than 200,000 labourers, were in the process of leaving the region, a local government official told Reuters news agency.
"In the interest of safety and security of the tourists and Amarnath Yatris [pilgrims], it is advised that they may curtail their stay in the [Kashmir] valley immediately," Kashmir's home secretary, Shaleen Kabra, said in a statement.
Security measures, including the deployment of 10,000 extra troops, were implemented by the Indian Government ahead of the Hindu pilgrimage.
India has long accused Pakistan of funding armed militants in Kashmir, a disputed territory claimed by both countries.
Militants have targeted Hindu pilgrims in the region before, most recently in 2017, when seven people were killed in an attack.
On Saturday, Britain and Germany warned their citizens against travelling to Kashmir.
Both India and Pakistan claim the Muslim-majority territory of Kashmir but control only parts of it.
The countries have been at war four times since the partition following the end of British rule in 1947, and Kashmir, located mostly in the Himalayan mountains, has been a key factor in the conflicts.
Tensions resurfaced in February when Pakistan-based militants killed 40 Indian troops in a suicide attack in Pulwama, provoking military clashes between the countries.