The gang entered the Spar shop on Lawnswood Road in Wordsley at around 10.40pm on Sunday and demanded cash.
They escaped with money from the safe and a till and also took a handbag.
No one was physically hurt in the robbery but those in store were said to be shaken by the experience.
So far nobody has been arrested over the raid.
A spokesman for West Midlands Police said: "We're investigating an armed robbery at Spar in Lawnswood Road, at around 10.40pm.
"Three masked men entered the store and demanded cash.
"The men, who were understood to be carrying a crowbar, axe and machete, escaped with money from the safe and a till. A handbag was also taken.
"Fortunately, although shaken, no-one was physically injured.
"We're examining CCTV and carrying out other enquiries to identify those responsible.
"Anyone with information that can help us should contact us via live chat on west-midlands.police.uk. Quoting 20/1659824/21."
The manager of the Spar shop declined to comment.