Windows have been smashed at the Old Parish Church and a framed picture hanging inside the church has been broken.
Rev Dave Whiteman said the vandalism has not angered parishioners “but has left us all deeply upset”.
He told the Observer there are eight holes across five panes of glass.
“Whoever did it must have thrown a brick with such force that it went through the window then broke a picture inside the church,” said the minister.
The vandalism happened overnight on Thursday and was discovered on Friday morning.
Rev Whiteman said: “Nobody benefits from vandalism.
“Mindless is the only word I can think of.
“It is just so upsetting.”
He said parishioners have told him nothing like this has happened at the church for more than 30 years.
However, in December 2018, Annan Old Parish Church was the focus of another investigation.
Three years ago, mindless thieves got away with the manger as the wee Baby Jesus was snatched from under the watchful eye of the Archangel Gabriel.
The theft of the Son of God from the Nativity scene shocked and outraged the town and made headlines around the world.
Despite an intensive search, the wee baby has never been recovered.