Police were alerted to the theft from the centre in Morrison Street around noon.
Urging the public to be vigilant of offers of the vaccine, they say they are pursuing a “positive line of inquiry.”
Chief inspector Neil Wilson said: “We were made aware of an isolated incident of theft of a Covid-19 vaccine from the vaccination centre at Morrison Street in Edinburgh around 11.50am on Saturday.
“The theft involved a single multi-dose vial of vaccine.
“A police investigation is ongoing, and officers are working closely with NHS Lothian and following a positive line of enquiry.
“Members of the public are reminded to remain vigilant to fraudulent offers of vaccine, which pose a risk to public health.
“Vaccines should only be administered by healthcare professionals as part of the national NHS Covid-19 vaccination programme.
“If you are offered a vaccine out with this setting you should decline and inform police immediately.”