Rescue workers with sniffer dogs are at the scene and said they had managed to rescue seven people so far.
One body has been recovered from beneath the tonnes of rubble, said disaster management officials.
Landslides are common in the Colombian Andes region – the latest was triggered by the heaviest rains in the country in four decades.
The Red Cross says 176 people have been killed by the rains this year and thousands have had to leave their homes.
Sunday’s landslide hit the La Gabriela district of Bello, north of Medellin, at 1900 GMT.
The BBC’s Jeremy McDermott in Medellin said local people were initially digging for survivors with their bare hands, after a large section of hillside fell onto the poor La Gabriela area of the city, in Antioquia province.
Emergency teams then arrived with specialist equipment and lighting.
Disaster official John Rendon said at least 50 people were missing but that the number could be higher.
“It was a mass landslide that buried more than 50 homes,” he told reporters.
One Red Cross worker, Cesar Uruena, said up to 200 people could be missing.
“We are focused on moving rubble to see if we find survivors,” he told the AFP news agency.
“The landslide buried 10 houses, each of then with three stories. Because on Sundays people usually have their family over for lunch, we think that on average there were between 15 and 20 people in each house,” Mr Urena explained.
Most major rivers in Colombia have burst their banks as a result of the heavy rain, and tens of thousands of people have been left homeless.
“This tragedy we are experiencing, not only in the Atlantic coast but across the country, has no precedent in our history,” said Colombian President Juan Manuel Santos, after flying over the western Atlantic region to assess the damage.
“We estimate that there will be more than two million people affected.”
Mr Santos has said recovering from the disaster is going to be very expensive, and that he is considering calling a national state of emergency if the rains continue.
“Unfortunately, this tragedy has just kept growing,” he said.
Our correspondent says the country’s emergency services are already struggling to cope with the scale of the disaster.
Neighbouring Venezuela is also experiencing heavy flooding.
Some 70,000 people have been driven from their homes there.
President Hugo Chavez has said his government plans to seize private land to house some of those forced to abandon their homes.
The May-November rainy season in Mexico, Central America and the northern part of South America has been extremely severe this year.
The extreme weather is attributed to the La Nina climatic phenomenon, which is caused by colder than usual water currents along the Pacific coast – BBC