Officers said hundreds of people may have witnessed the stabbings in Union Street at about 5.50pm on Friday.
The first man was stabbed outside Sainsbury's and the second was found slumped outside Boots. Minutes later, a 23-year-old man was arrested in New Street. He remains in custody. Post-mortem examinations on the two men, both in their 30s, were due to take place.
Big Issue founder and editor John Bird said everyone at the magazine was "absolutely devastated".