It has been reported at least two children were on board but it is believed they survived the crash and had already been taken to hospital.
The incident occurred about two kilometres from the local airstrip though it is not yet known if the aircraft was landing or taking off.
Emergency authorities and the Federal Aviation Administration are investigating the cause of the crash.
"A single-engine Piper PA-32 with six people aboard crashed under unknown circumstances into a residential backyard in West Jordan, Utah, Saturday afternoon," the FAA said in a statement.
The administration urged people to contact local authorities for information on the condition of those involved in the crash.
FAA Statement on aircraft that crashed into a residential backyard in West Jordan, Utah, Saturday afternoon. Information is preliminary and subject to change. pic.twitter.com/ZRfLM9sfoE