Christopher Dorner was shot at by a fish and game ranger, as he fled in a stolen vehicle in north-east Los Angeles, Reuters is reporting.
The agency states that earlier Dorner had broken into a home, tied up a couple and stole their pick-up truck.
Local media is also reporting it is believed one of the hostages was able to flee and raise the alarm.
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Police said the child, who was without a driving licence, was trying to make his way 2,500 miles from the east coast to Perth.
The 24-year-old was charged with 14 counts of wounding with intent to do grievous bodily harm and one count of throwing a corrosive fluid.
Winds will veer northerly overnight with colder air streaming in over the next few days.