The 20-year-old, from the Castleton area of Gwent, was detained following the discovery of two bodies in Queen Street, Cardiff, at 5.50am on Wednesday.
South Wales Police believe the suspect was known to the victims, a man and a woman, and are not looking for anyone else in connection with their deaths.
Matalan confirmed the 21-year-old woman and 33-year-old man, who both lived in Cardiff, were employees at its Queen Street store.
The incident happened just two hours before the shop was due to open at 8am.
Matalan chief executive Jason Hargreaves said: “It is with great sadness that we can confirm that there was a fatal stabbing in Queen Street, Cardiff, this morning.
“Police discovered the bodies of a man and a woman outside the premises at 6am and arrested one man, who is currently in police custody.
“Both of the victims worked at our Cardiff branch so understandably all of our colleagues are receiving our full support. We request that they are given the space to deal with this at this difficult time.
“That is all we know at this stage and we are working tirelessly with the police in their investigations.
“We extend our condolences to the families of everyone involved.”
The suspect was arrested with the assistance of Gwent Police officers at an address in Castleton within an hour of the incident being reported.
He is currently being held at Cardiff Bay police station.
A spokesman for South Wales Police said the identities of the victims have been established and their families informed.
Post-mortem examinations will take place to determine the causes of their deaths.
Chief Superintendent Belinda Davies, of South Wales Police, said: “This incident occurred in the main shopping area in the heart of the city in rush-hour and it has no doubt shocked the community of Cardiff.
“Please be reassured that we have a team of officers investigating what happened and importantly we have a suspect in custody and we are not looking for anybody else.
“We are in the very early stages of the investigation but I would like to add that at this stage we believe the suspect was known to the victims and it was not a random assault.
“I would like to dispel speculation circulating as to the motive behind this tragic incident and make it clear that this is not being linked to terrorism, and any links to the homeless community are unfounded.”
A large section of Queen Street, the Welsh capital’s main shopping thoroughfare, was cordoned off.
Members of the public were unable to access much of the pedestrianised area, which was being treated as a crime scene.
Stores including Topshop, Zara, River Island, Boots and Primark, did not open on Wednesday morning.