According to police, the email was received by AH Bhat, a hotelier of Devi Grand hotel, on November 24 threatening to target the shrine to avenge the hanging of Kasab.
"Investigation is going on...We cannot rule out either of the two angles to it, one hoax, the other threat from the terror outfit," a senior police officer said.
"We cannot deliberate on the issue further since preliminary investigation into the matter is going on," he added.
The cops have seized the computer and other equipments on which the email had been sent.
Efforts are on to decode the email, police said.
Jagjeet Kumar, Deputy Inspector General of Udhampur-Reasi and other senior officials of central agencies visited Katra and reviewed the security arrangements there.
Meanwhile, an alert has been sounded in the region with additional security being put in place.
The cops have intensified frisking people, checking of vehicles and keeping an eye on suspected movements.
The email could be a prank by some anti-national elements but no chances can be taken, the senior police official said.