They described it as "very dark, brutal, and gratuitous with no positive messaging", and "inappropriate" to be shown to a school community.
They questioned the moral message portrayed in the musical, and said it was the culmination of a trend towards productions of an adult nature that had sparked concerns among parents.
In response, St Kentigern head of college, Steve Cole, said the school was committed to going ahead with the production but would be "very mindful of the concerns you raised".
"The College Sweeney Todd production is the school edition of the musical and indeed has recently been performed by a number of New Zealand and Australian schools," it said.
Scenes deemed to be of a mature nature would be "staged in a way which takes into consideration the age of the performers without compromising the integrity of the show", Mr Cole said.
One father who signed the letter said there was "absolutely no concerns at all from a health and safety perspective", pointing to the "pretty dark" themes in Sweeney Todd and how it sat within a Christian school.
A St Kentigern College spokeswoman declined to comment on the letter, saying the incident was still under investigation.