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Iggy Azalea and Playboi Carti's rental home was burglarized in Atlanta ... and the couple told cops a massive amount of jewelry was stolen!!!

Law enforcement sources tell TMZ ... officers responded to a residential burglary Sunday, and Iggy told cops a thief found a way into the couple's Buckhead mansion a few days before and made off with tons of bling.

Our sources say the missing items include custom rings, chains, bracelets, pendants, watches, earrings and even a diamond engagement ring. The missing jewelry is a mix of gold, diamonds, silver, platinum, pink sapphire and rose gold.

We're told the amount of missing jewelry is worth a whopping $366,000!!!

Our sources say Iggy told cops she was alone inside the home when the burglary went down, and she heard footsteps in the house but didn't think much of it at the time. Iggy told police it was raining, and she left a back door unlocked so Playboi Carti could get in the house ... and she also told cops she thought the thief had a gun.