The department issued an amber-coloured alert, indicating severe weather for parts of Jammu and Kashmir, Uttarakhand, Himachal Pradesh, Haryana, Delhi, Chandigarh, western Uttar Pradesh, Sikkim and West Bengal.
"Thunderstorm accompanied with squall (wind speed reaching 50-70 kmph) and hail is very likely at isolated places over Himachal Pradesh and Uttarakhand. Thunderstorm accompanied with squall (wind speed reaching 50-70 kmph) is also very likely at isolated places over Haryana, Chandigarh, Delhi, West Uttar Pradesh and sub Himalayan West Bengal and Sikkim," read the advisory issued by the department.
Authorities in Haryana have closed schools on Tuesday following storm warnings.
The Delhi government too has decided to shut all second shift schools starting on Tuesday afternoon.
Officials said on Monday night a dust storm, with a wind speed of 70 km per hour, hit the national capital followed by a squall, bringing down the temperature.
The traffic police in the capital city has asked commuters to check weather conditions before travelling. Delhi Metro, too, has decided to exercise extreme caution in running of trains in the wake of the warning.
According to the Met Department, thunderstorm accompanied with gusty winds, is very likely at isolated places over Punjab, Assam, Meghalaya, Nagaland, Manipur, Mizoram and Tripura, Bihar, western Madhya Pradesh, east Uttar Pradesh and East Rajasthan, Coastal and South Interior Karnataka, Tamil Nadu and Kerala.
Last week, at least 124 people were killed and more than 300 others injured in five states due to dust storms, thunderstorms and lightning.