The Shuker Field off Audley Avenue in Newport, where Nova United play, is gouged with tracks seemingly caused by small vehicles.
The club said that four of the field's six pitches have been damaged. The team is due to begin its next season on January 10.
A statement said: "As if the current pandemic isn't a strain on grassroots football enough, we now have this to deal with.
"It is disappointing that an individual or group of people have decided to tear up our pitches just as we are getting ready to return in the new year."
Police in the town said that they received reports of the antisocial use of off-road motorbikes and quads earlier this week, before the damage at Shuker Field was discovered today.
The football pitch is often used by pupils at the nearby Burton Borough School.
Newport's police Safer Neighbourhood Team appealed on social media: "Help us find those responsible before anything else is damaged or someone gets hurt.
"Info to email@example.com or @CrimestoppersUK – 0800 555 111."
Information about non-emergency crime can be reported to police on 101.
Reports the last few days of off-road bikes & quads causing problems in the area, & today this on Shuker Field.— Newport SNT (@NewportCops) December 31, 2020
Help us find those responsible before anything else is damaged or someone gets hurt.
Info to firstname.lastname@example.org or @CrimestoppersUK 0800555111 pic.twitter.com/wb83g6Z40L