Police were called to the Interfaith Peace Chapel on 5 January 2017 after the graffiti was discovered on three panels of its pale external walls.
Sprayed in black were a Louisiana phone number, a reference to a "brown chivy suburbin" car, the words "kitty porn" and the name "Johntion kimbrou".
It forms part of the Cathedral of Hope, which has a predominantly LGBT congregation, in the Oak Lawn area of Dallas.
Neil Cazares-Thomas, the cathedral's senior pastor, called the vandalism an "act of hate".
"At first we thought it was just vandalism, but on reflection we're not sure whether it was vandalism or whether we were targeted," told local news station Channel 33.
"To see graffiti on the side of any building is never pleasant," he added. "To see graffiti on the side of your own building is devastating."
The pastor revealed that this is not the first time the building has been graffitied – someone previously sprayed "666", commonly associated with the devil, onto its side.
It is also not the only chapel of architectural note to have been purposefully damaged in recent memory.
In 2014, vandals sacked Le Corbusier's Notre Dame du Haut chapel – considered one of the fellow modernist's most important works.
It hasn't been a good 12 months for Pritzker Prize-winner Johnson's work. The American architect's interior for The Four Seasons Restaurant in New York suffered a blow when furniture and tableware designed for the space was auctioned off, in a move slammed by critics.
Also last year, a book was released that detailed his impassioned support of Nazism.