Alicia Arengngma, daughter of a policeman, was buried when debris of a landslide following heavy rain blocked the ground floor of Meghalaya police's CID complex, police said.
Some nearby houses were also damaged and rescue operations were on, official sources said.
The injured were admitted in a government hospital.
Incessant rain over the past couple of days has thrown normal life completely out of gear in the state.
Several parts of the low-lying areas of the hill station, especially Polo Grounds area were inundated due to heavy rain with Umkhrah river in full spate. Many houses and market places in the area were partially flooded.
Minor landslides and subsequent road blockades were reported from several parts of the state even as the situation began to improve late in the afternoon with the rains receding for the time being.
Meanwhile, the Met office has predicted heavy to moderate rains over the next 24 hours throughout the state.
Cherrapunjee (Sohra), has been experiencing heavy rain over the past week with the rain-gauge reading an average of over 30 cm on a daily basis.