Police said the death toll could rise.
Seven people are also missing after the equivalent of a month's rain fell overnight, loosening slopes already saturated by heavy rain over the past few weeks.
One resident said: "There was rain and thunder all night, beating down so hard I was scared to go outside. I've never seen anything like this."
Helicopters hovered overhead, lifting out survivors, as rescue workers searched through mud and piles of stones in residential areas about three miles from the city centre.
Among those dug out of the debris were two brothers, aged 11 and two, whose house was struck as they slept.
Houses had been pushed 100 yards by the landslide in the worst-hit area, where thick, knee-high mud hampered rescue efforts.
Hiroshima city authorities issued an evacuation advisory notice about an hour after the first landslide.
An official at the city's fire department said: "Something went wrong in our analysis (of the situation). We failed to issue an evacuation advisory ahead of the disaster. Looking back, I believe this is something we need to amend".
Cities in land-scarce Japan often expand into mountainous areas, leaving such development vulnerable to landslides.
About nine inches of rain fell in the area in the 24 hours up to yesterday morning, a record-breaking level equivalent to a month's rain in August.