The exact time the vandalism occurred is not clear.
A caller to radio station 3AW, named Philip, witnessed the vandalism earlier on Thursday morning.
“The window is broken, not completely shattered,” he said.
“There’s spray paint all over the front.”
A spokeswoman for Victoria Police said authorities were investigating the “criminal damage incident”.
“Investigators were told an office building on Princes Highway was graffitied and damaged by an unidentified person,” she said in a statement.
“An investigation is underway and police urge any witnesses or anyone with information to contact Crime Stoppers on 1800 333 000.”
Mr Andrews’ office is in his suburban electorate of Mulgrave. He was elected to represent the area in 2002.
On Wednesday, the Premier acknowledged the deep frustration felt by some at the length of the strict lockdown and said he was aware the social and economic costs may outweigh the benefit of the measures if they lasted too long.
“These measures come with a cost. There is a public health benefit, but there is also a cost,” he said.
“This is not an indefinite arrangement … At some point, the cost of the restrictions will be greater than the increased risk and the increased challenge for our public health team to keep the virus suppressed if we open earlier than we had planned.
“Some of those [costs] are measured at a very personal level, in terms of the health, both physical and mental, of individual Victorians and their families. Then there’s obviously a whole range of economic considerations beyond health.
“Weighing up those matters is very, very challenging but there is an enormous amount of thought, consideration and judgement that comes with that task.”