Chicago Cubs spokesman Peter Chase said the graffiti was reported to the organization Sunday and it was mostly removed by 8 p.m. the same day, the Chicago Sun-Times reported Monday.
The Chicago Tribune said the graffiti appeared to begin with the word "Sox," an apparent reference to the Chicago White Sox, and a second illegible word.
Chase told the Sun-Times an investigation has been opened into the incident.
"We are presently in a fact-finding stage when it comes to any other details," he said.
The statue, which was moved a block north from its original home at North Sheffield Avenue and West Addison Street in 2010, has been targeted by vandals in the past. Dead goats were found hanging from the memorial to Caray, who died in 1998, in an apparent attempt to break the Cubs' "Billy Goat curse."