The banknote was delivered to Bletchley Post Office to commemorate the work done by Mr Turing and his team at Bletchley Park.
The Bank of England banknote entered circulation on Wednesday.
Ahmed Butt, postmaster for Bletchley Post Office in Buckinghamshire said: “Many of my customers feel more comfortable dealing in cash.”
The Post Office network maintains more than 11,500 branches. On average, over £2 billion of cash is withdrawn and deposited every month at them.
The Post Office recently launched a “save our cash” campaign.
Amanda Jones, retail and franchise network director at Post Office said: “We’re so pleased that Bletchley Post Office is one of the first places to have the new £50 note today.
“What happened less than a mile away at Bletchley Park helped end World War Two and Alan Turing played such a pivotal role as a codebreaker. It’s a fitting tribute that he’s the face of this new note.”
Research from ATM provider Cardtronics found that 43% of 18 to 24-year-olds often want to pay in cash, but are forced to use alternatives when shops will not accept it.
Marc Terry, international managing director for Cardtronics said: “Our latest research shows as many as three-quarters (74%) of UK consumers believe that all retailers should offer the option to pay in cash.”