Two teens were busted for snatching a dachshund named Milkshake from a Bronx apartment last month — but the beloved emotional support service dog remains missing, authorities said Tuesday.

A boy and girl, both 16, were nabbed Monday and also accused of trying to shake down Milkshake’s heartbroken owner, who lives in the same building as them, cops said.

“As of right now, Milkshake is not recovered,” Chief of Detectives Joseph Kenny told reporters during a Tuesday briefing. “They inform us that Milkshake ran away. We checked all the shelters who still have posters up, but Milkshake is nowhere to be found.”

Owner Luz Montanez, 34, previously told The Post that her “baby” Milkshake, a 10-year-old female dachshund, was scooped up by the heartless thieves while she was distracted with her young son’s birthday party on May 4.

Video released by the NYPD last week shows the pint-size pooch following the two dognappers along the hallway, up and down a small flight of stairs and toward the door of the building on Tiffany Street near Westchester Avenue in Longwood.

Montanez hung up posters around the neighborhood imploring for someone to help bring Milkshake home — and that’s when the alleged thieves contacted her at one point, Kenny said.

The cold-hearted kids demanded Montanez CashApp them money in return for her stolen pet, according to the chief. 

 “The two perpetrators do call her, try a little bit of extortion,” Kenny said. “[They said,] ‘We’ll give you your dog back if you give us money.’”

Other kids also started barraging Montanez with harassing phone calls.

“Kids start calling her, start messing with her, start fooling with her,” Kenny said.

The suspects live in the same building with Montanez, he added.

Milkshake had not been returned by Tuesday and her whereabouts were not known, police said. 

“I don’t believe the dog ran away,” Kenny said. “Either they gave it to somebody or sold it.”

 The cruel teens, whose names were not released because they are minors, are charged with third-degree grand larceny and second-degree harassment.

Montanez, who couldn’t immediately be reached Tuesday, had said the suspects “look familiar,” based on the surveillance video, but she did not know them personally.

She was hosting a Bluey-themed birthday party inside the apartment for her kindergartner son, and let the kids into the hallway to play, with Milkshake later joining them, Montanez said. 

But by around 7:50 p.m., as Montanez served cake to the guests, she realized the brown pooch was gone.

“It just doesn’t make sense why you would do that and then choose to pick on me and harass me and do all these things,” the stricken dog-owner said last week. “For what? I’m a quiet tenant. I keep to myself. I don’t make a ruckus. I don’t do much but stay in my lane. And just don’t understand why this has happened.”

Milkshake was only 3 weeks old when Montanez received her as a birthday present from her dad – and even bottle-fed the pup and kept her baby teeth in a jar.

“Milkshake is legit the first child. I call her my favorite,” the distraught owner said. “I mean, both of my kids are my favorite… I tell her, ‘You’re my favorite dog. And I tell my [son], ‘You’re my favorite human.’ These are both my kids!

“This is my baby. This is my soulmate,” Montanez added of her beloved pet. “This is my heart, my heartbeat. She’s been through everything with me.”

Montanez said last week she hopes someone with good intentions will return her dog.

“People who are dog people don’t do things like what they’ve done,” she said of the thieves. “It’s mean, and nobody does that. I know your intentions for the dog are not pure.”

“I need someone to hear me because she needs to come home,” Montanez said in a desperate plea. “She needs to come home already.”