Three shops were raided between April 19 and 25, with two shops in Wolverhampton being targeted and another in Bloxwich.
A spokesperson for West Midlands Police said: "We've arrested a man on suspicion of three armed robberies across Walsall and Wolverhampton.
"These happened at shops in Cresswell Crescent, Bloxwich; Griffiths Drive; Wolverhampton and Stafford Road, Wolverhampton; between 19-25 April.
The spokesman added: "A 32-year-old man was detained and has since been bailed with conditions while enquiries continue. Anyone with information can contact us via Live Chat on our website and quote 20/313896/22."
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org