Ms Wells said she would report the incident in Glasgow to police.
She tweeted a picture of the graffiti, sprayed in red paint on the wall of her office in Maryhill Road, adding: “Happy new year! A civic and joyous start to 2020 at our constituency office.”
A spokesperson for the MSP said: “It’s depressing that abusive graffiti like this has become the norm for MSPs and MPs across Scotland.
“It’s not a particularly nice way to start the year but it won’t stop Annie from continuing to get things done for her constituents and people in Glasgow.”
Ms Wells contacted police last year over fears for her safety after she received online threats and abuse.
During the general election campaign, SNP MSP Aileen Campbell’s office also experienced vandalism when a window was smashed and “SNP out” was spray-painted on her office.
Ms Campbell, who is the Communities and Local Government Secretary, said at the time she was “deeply saddened” by the attack.
Additional reporting by agencies