Spokesman Ronald Smith said a similar envelope was delivered this afternoon to the Salt Lake City Mormon temple.
The L.A. Mormon Temple was voluntarily closed. Employees were evacuated as a precaution.
The incident was treated as a potential hazardous-materials situation. The FBI was on the scene and a hazardous-materials team inspected the envelope in what was described as a routine field test.
The L.A. City Fire Dept. was also on scene Thursday evening. LAPD officers were also part of the investigation.
There have been no reports of injuries.
An concurrent investigation is under way in Salt Lake City.
City News Service contributed to this report.