Four people have been rescued from under the garbage dump, they said.
According to the officials, a car, a scooter and two motorcycles, which were moving on a nearby road, fell into the Kondli canal after the garbage dump collapsed this afternoon and pushed the vehicles off the road into the canal.
"Two persons, Raj Kumari (32) and Abhishek (22), have died and four others rescued," a senior police official said.
According to a fire department official, initially four fire tenders were rushed to the spot but later 11 more vehicles were sent.
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The landfill site falls under the jurisdiction of the EDMC (East Delhi Municipal Corporation).
East Delhi mayor Neema Bhagat, when contacted, said a portion of the garbage mound collapsed due to rains.
"A portion of that (collapsed garbage mound) then fell into one of the canals close to it and the water splashed on to some moving vehicles throwing them into another flank of the canal," Bhagat claimed.