A beloved pet chihuahua stolen from outside a shopping centre in Adelaide's CBD earlier this week has been reunited with its owner, after police tracked it to the alleged thief's home.

Key points: Ruth Reidy's black and white chihuahua was stolen on Tuesday

Ruth Reidy's black and white chihuahua was stolen on Tuesday Ms Reidy sells The Big Issue alongside her dog in Rundle Mall

Ms Reidy sells The Big Issue alongside her dog in Rundle Mall Police arrested and charged a Richmond woman with theft on Friday night

Ruth Reidy, who works as a vendor for The Big Issue, had her black and white chihuahua Fifi stolen from outside Woolworths in Adelaide's Rundle Mall at about 2:00pm on Tuesday.

Ms Reidy, 70, said she left Fifi, sitting in a pram and wearing a white dress with black stripes, at the supermarket's checkout area for two minutes, after finishing her shift.

The small dog is a well-known sight in Adelaide's main CBD shopping strip.

But just three days later, on Friday night, police confirmed the dog had been found and a woman had been arrested over the theft.

Following investigations, police visited an address in Richmond, just west of the CBD, where they found Fifi and arrested a 43-year-old woman.

The woman was charged with theft and bailed to appear in the Adelaide Magistrates Court at a later date.

During the investigation, police released CCTV footage from the corner of King William Street and North Terrace in the CBD showing a woman carrying a dog across the busy intersection.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 28 seconds 28 s Police CCTV of a woman holding a dog crossing King William Street.

Earlier this week, Ms Reidy said she had been "praying to God" for Fifi's return.

Fifi and Ms Reidy featured in The Big Issue's 2019 calendar.

The magazine — which gives homeless and disadvantaged people a chance to help themselves by working as vendors — was first sold on the steps of Melbourne's Flinders Street Station in 1996.

Restored 'faith in humanity'

The Big Issue state operations manager Matt Stedman said the find had restored his "faith in humanity".

"I think on a personal and individual level, I think for Ruth … this is a really important thing for her," he said.

Ms Reidy was reunited with Fifi late on Friday night. ( Supplied: Nat Rogers )

"For Ruth, [Fifi] is a companion, but for her, it's become a really good talking point for her to engage with people around her.

"It gets really hard … you are quite isolated and alone and I think having Fifi with her is that chance to break down the barriers."

Mr Stedman said this was one of the worst things that had happened in his time with The Big Issue.

He said the find had showcased how well the police and community members could work together.

"It was great to have the police so quick on the scene, they were great in communication," he said.

"The power of the community was so fantastic in getting the word out and helping us come to a great resolution."