Suri Cruise -- Aye Dios Mio! ... ¿Dónde Está Mi Chihuahua?

Suri Cruise's new Chihuahua, Honey -- which she's only had for a couple of weeks -- has disappeared ... and TMZ has learned there's a $1,000 reward for the pup's return.

Sources close to the situation tell us ... Suri and her mom, Katie Holmes, took Honey to a friend's house in Beverly Hills Sunday ... where the pooch slipped out the front gate. We're told she wasn't wearing a collar because they removed it to take her swimming.

50 reward posters have been plastered around the area. They even issued a pet Amber alert -- to notify houses in the area about the disappearance. We're told Honey also answers to Maple -- her name before she went to live with Suri.

Time is of the essence in the search -- the area where Honey/Maple bolted is heavily wooded and a known coyote hotspot.

Katie and Suri adopted the 1-year-old Chihuahua mix from a Studio City rescue ... shortly before moving into their new digs in Calabasas a couple of weeks ago.