Investigators are still probing what killed John Gerrish, his wife Ellen Chung, their one-year-old daughter Miju and their dog last month.
Their bodies were found on a remote hiking trail in the Sierra National Forest in Mariposa County on 17 August.
Federal park officials have now closed several recreational sites and trailheads around the Savage Lundy Trail for a month “to provide for public safety” amid “unknown hazards”.
Anyone using or being found near the trailheads is subject to fines up to $5,000, or $10,000 if they are in a group.
Officials say that the trails and campgrounds will remain closed until at least 26 September.
Investigators are still unsure what killed the family, but have ruled out hazardous gases coming from a nearby mine.
They have also looked into whether toxic algae blooms may have caused the deaths.
“This is a very unusual, unique situation,” Kristie Mitchell, a spokesperson for the sheriff’s office, said in a statement last week.
“There were no signs of trauma, no obvious cause of death. There was no suicide note.”
Mr Gerrish, a British-born software designer from San Francisco, and his wife had bought several homes in Mariposa County after reportedly falling in love with the area.
“We know the family and friends of John and Ellen are desperate for answers, our team of detectives are working round the clock,” Sheriff Jeremy Briese has said.
“Cases like this require us to be methodical and thorough while also reaching out to every resource we can find to help us bring those answers to them as quickly as we can.”
Police say that toxicology labs were conducting tests on the family and their dog.
Samples of water found around the trail area and of water the family had with them have also been sent to the State Water board and independent labs for testing.
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