The incident occurred around 3.45pm in the municipality of Urdorf, west of the city, Zurich cantonal police said.
The crane, erected on a building site, fell onto an apartment building causing extensive damage, police said in a statement.
Residents of the building were forced to stay in a municipal shelter overnight, the statement said.
“I was shocked and feared for my family,” a relative of residents living in the damaged apartment building told 20 Minuten newspaper.
After severel phone calls he learned that his parents and brother escaped injury from the accident, the daily said in a report on its website.
A man was slightly injured from the crane’s collapse, police said.
Police and forensic experts have launched an investigation into the cause of the mishap.