Los Angeles Police said the costume, valued at about $325,000 (£240,000), vanished from a prop storage warehouse in Pacoima.
It is believed to have disappeared between February and 25 April.
However, Officer Christopher No, a spokesman for the Los Angeles Police Department, said the famous red and gold suit had only been reported missing on Tuesday.
Downey wore the suit in the original Iron Manfilm directed by Jon Favreau and released in 2008.
After a tough opening weekend, the film went on to earn $585m (£431m) at box offices worldwide.
It was the first instalment of the multi-billion pound Marvel Cinematic Universe.
Other costumes were used in later movies related to the Avengers franchises.
Mr No said the “unusual” theft was considered high priority, but there were no leads in the case so far.
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No other items were reported missing from the warehouse.
There is no word on whether the Avengers have assembled to join the search.