A section of wall at the memorial in Gloucester Park was spray painted overnight on Monday, Gloucestershire Police said.
A spokeswoman said the graffiti appeared some time between 17:00 GMT and 07:00 GMT on Tuesday.
The monument remembers people from the city who died during both World Wars and the Korean War.
The spokeswoman said: "This graffiti tag is used regularly around Gloucester and we are eager to trace the offender.
"Vandalising the memorial is very disrespectful and will not be tolerated by police."
The memorial is due to be used for the annual Remembrance Sunday event on 13 November.
Part of a war memorial has been vandalised a few days before Remembrance Day.