Authorities have asked people living near the river to leave their homes and move to safer places.
At least 10 people are missing after landslides buried a number of houses.
The alert comes after more than 250 people died in September in what was described as the worst flooding in the region in half a century.
The deputy chief minister of Jammu and Kashmir state, Nirmal Singh, said the authorities were on "full alert" after heavy rain in the Kashmir Valley and the "situation is being monitored continuously".
Senior police official Javid Mujtaba Gillani told the AFP news agency that rescue workers were trying to find out "10 to 12 people" buried under mudslides in Chadoora, some 15km (10 miles) west of the main city of Srinagar.
More than 200 families have been moved from low-lying areas to tents, government buildings and to the homes of their relatives on higher ground.
Many areas of Srinagar are already under water.
The main road connecting Srinagar with Jammu has been closed following landslides and authorities have issued avalanche warnings in seven districts, reports say.
Forecasters are predicting more rain this week.
Last September's floods affected more than 1.2 million people and damaged more than 180,000 houses in the state.
A flood alert has been issued in Indian-administered Kashmir following torrential rain and a surge in the water level of the Jhelum river.