Los Angeles Fire crews responded to the scene in the 1400 block of West Sunset Boulevard just before 8 a.m.
The fallen tree downed utility lines and significantly damaged the structure, which sits atop an embankment.
"We saw that there was a tree that broke into our roof, and the noise was incredible, apocalyptic," homeowner Vince Meghrouni said.
The transient, who has not been identified, was rescued after about 30 minutes, Los Angeles Fire officials said.
"It actually turned out that there was a homeless man right underneath, living underneath the tree, so he got caught and pinned under there," witness Ricardo Moet said. "When it happened, I ran up those stairs right there to go and check out and see if anybody was in the house or got injured or anything."
The man was transported to a local hospital with minor injuries but is expected to be OK.
The house is a different story. The family will need to find temporary housing just before the holidays.
"Find out how long we're gonna be out. I imagine it'll be a while, and figure out what we're gonna do for lodging," Meghrouni said. "We got the wherewithal, just gotta figure out what you can do."
The home has been red-tagged, which means residents are not allowed to enter. Another unit in the duplex has been yellow-tagged.
City News Service contributed to this story.