Police said the incident at the office in the Loreburne Shopping Centre, High Street, was captured on CCTV.
Constable Dale McEwan said: “We have CCTV footage of a male person, wearing a dark jacket with a hood up and jeans, smashing the window at around 3am on Monday.
“The person is then seen to run down towards Dock Head.”
Ms McAlpine, a South of Scotland MSP, shares the Dumfries shop with fellow Nationalists Aileen McLeod MSP and Richard Arkless MP.
Writing on Twitter on Monday, Ms McAlpine said: “My constituency office was deliberately targeted by man with brick at 3am. He’s on CCTV. I will not be intimidated.”
Police have not said whether they believe the office was deliberately targeted.
Anyone with information is asked to call officers on 101.
SNP MSP defiant after constituency office window smashed