Thirty homes collapsed in different sectors of the city in the early hours of Wednesday.
The landslides happened after the monthly average of rain fell in one night, the city's mayor said.
Earlier this month, more than 300 people were killed in landslides in Mocoa, in southern Putumayo province.
The mayor of Manizales, JosÃ© Octavio Cardona, said he feared the number of dead could rise further.
The mayor tweeted that President Juan Manuel Santos was on his way to the city to inspect the situation.
He said that the worst affected areas were those built on steep hills.
At least seven people have been killed and 20 are missing after heavy rains caused landslides in the city of Manizales, in central Colombia.