Afterwards the band, Finaghy True Blues, from south Belfast defended the music.
They admitted they had played the hymn How Great Thou Art.
They said they were only playing religious music outside a place of worship.
Finaghy True Blues were one of a number of bands that passed the church on Monday morning.
All others observed the ruling, which was displayed on the side of a police Land Rover.
More than 3,000 police officers are on duty at Orange Order parades across Northern Ireland.
The Parades Commission issues determinations on contentious marches in Northern Ireland.
In April, 13 members of a loyalist flute band were convicted of provocatively playing a sectarian tune  outside St Patrick's Church.
The Prince of Wales and the Duchess of Cornwall visited St Patrick's Church as part of its 200th anniversary celebrations in May during a two-day visit to Northern Ireland.
A flute band has played a hymn tune going past St Patrick's Catholic Church in Belfast in spite of a Parades Commission determination that only a single drumbeat should be played.