Police said the break-in at St Mary's Cathedral in York Place was a "despicable theft".
Officers think two men entered the church at 2.30am on Saturday before taking the safe containing thousands of pounds in cash.
The men were described as white and aged between 20 and 30. One was wearing a dark jacket, jeans and white trainers.
The other had a dark hooded top with white stripes on the sleeves and was carrying a dark rucksack.
St Mary's Cathedral is Scotland's largest, and home to the Diocese of Edinburgh.
Detective Sergeant Clark Martin said: "This is a despicable theft from a popular place of worship and city-centre attraction.
"We would urge anyone who remembers seeing any suspicious activity around St Mary's Cathedral or within York Place in the early hours of Saturday morning to contact police immediately.
"In addition, anyone who recognises the description of the suspects or who has any other information relevant to our ongoing enquiry is also asked to get in touch.
"Those with information can contact Police Scotland on 101 or alternatively, the charity Crimestoppers on 0800 555 111."