Most Rev John Davies, Archbishop of Wales, was supposed to preach at the service, calling on civic leaders from across Wales to follow the example of St David.
Archbishop John was expected to give the address at St John the Baptist Church in Cardiff.
However, a mini-service led by Canon Sarah Rowland Jones will be held instead for anyone who turns up.
Speaking of the importance of marking St David's Day, Archbishop John said in a statement, "St David founded communities where people worked, with whatever resources they had, to create trusting, supporting and lasting relationships in which everyone felt secure, supported and valued.
"It took ongoing hard work and a deal of self-discipline but he was, I believe, a model we would do well to emulate in our own communities today where some feel less than valued, vulnerable and insecure."
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