The granite headstone, a replacement for an original tombstone which went missing in the 1950s, was daubed with graffiti just days before it was due to be officially unveiled.
The memorial to the architect - the influential designer behind many of Glasgow's impressive Victorian buildings - was erected in the city's Southern Necropolis, in the Gorbals area, last September.
However, a carving on the tombstone, which was designed by architecture students Graeme Andrew and Edward Taylor, has only just finished.
Despite the attack, the completed headstone is still expected to be publicly unveiled at a ceremony on 25 May.
In a separate incident, previously reported in the AJ, vandals repeatedly attacked the Stirling-shortlisted Phoenix Initiative in Coventry, forcing the design team to go back to the drawing board ( Vandalism forces a redesign on the Phoenix Initiative).