The Archdiocese of Glasgow has condemned a "shameful attack" on the city's third oldest church.
Police Scotland were called to St Simon's in Partick at about 16:20 on Monday.
Pictures posted on the church's Facebook page show the damage, which included a broken Jesus statue.
Police are investigating but officers said there was nothing at this stage to suggest the incident was sectarian or a hate crime.
A post on the Archdiocese of Glasgow Facebook page said: "Whatever the motive this is a shameful attack on a much loved church.
"Let's help find those responsible. This kind of activity is unacceptable."
The attack has been widely condemned on social media.
Comic book writer and artist Mark Millar tweeted: "This is demonic. Canon McBride is a fantastic priest.
"Terrible he had to walk in and find his church desecrated like this."