The Los Angeles Police Department announced Saturday they've arrested Sadie Slater ... a 21-year-old L.A. resident on a robbery charge for her alleged involvement in the crime. Her bail is set at $70,000, according to the LAPD.

We've confirmed the arrest with law enforcement sources ... who added they've been trying to find out the dog's location from the suspect.

Remember ... the victim Ali Zacharias was eating lunch in DTLA last month when a woman came up, grabbed her dog Onyx's leash, and started to walk away with him. Ali gave chase before the alleged thief jumped into a car.

AZ leaped onto the hood of the thieves' getaway car and was driven around for several blocks, fearing for her life before the vehicle made a sharp turn and loosed her from the front.

We spoke with Ali earlier this week ... who told us police were starting to take her case seriously when all of the media attention spotlighted it.

Well, cops are certainly taking it seriously ... with their first suspect in custody.