Nicole Bailey, 23, picked up the cash at a branch of One Stop, in Blurton, Stoke-on-Trent, after it was dropped by a customer who withdrew it from a nearby cash point, police said.
Bailey pleaded guilty at North Staffordshire Justice Centre after seeing CCTV evidence.
Her defence team reportedly argued the case should have been dealt with through a police caution.
Bailey, of Highfield Drive, Blurton, must also pay £20 compensation, a £20 victim surcharge and £135 in court costs.
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The theft occurred on 8 August last year.
Ch Insp Karen Stevenson, from Staffordshire Police, urged anyone who finds lost money to "do the right thing".
"Morally, the right thing to do is hand in any found property so that the person who has lost out has every opportunity to be reunited with it."
"This was someone's hard-earned money and we are committed to supporting all victims in our community."
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