It is thought that the tree was vandalised at some point after 7pm on Sunday, 11 December.
Sections of lights were ripped from the tree causing the remaining lights on the tree to stop working.
PCSO Stephen Connolly said: "It would appear that some drunken buffoon has taken to damaging [the tree] over the weekend. Sections of the lights have been ripped off the tree causing most of the other lights to not work as well as the wooden panels having a hole punched/kicked into it & a strip of wood being ripped off.
"Both Preston City Council & Preston BID have spent money on making Preston look fantastic this time of year and the last thing the City Centre needs is someone wasting time & money to repair such displays after mindless damage.
"Remember causing damage is a criminal offence and can see you arrested & put in front of the courts which could see a maximum of 3 months imprisonment or Â£2500 fine. Alternatively officers could choose to give you a Â£90 on the spot fine, the last thing you want less than 2 weeks until Christmas."
Police officers are currently reviewing CCTV footage from the area.