Members of Newport Salop RFC said they had been left feeling deflated and angry after the incident, believed to have taken place on Monday night.
The club had only recently re-seeded the pitch at great cost but wheel spins left chunks dug out of two pitches at the Old Showground, Forton Road, areas used by the club's youngsters.
"We are absolutely gutted about this," said bar and catering manager Andy Bowsher.
"Somebody has been driving in a car over the second and third team pitches and has basically performed doughnuts on them.
"We had just laid new seed on the pitches, at great expense, in preparation for the season.
"I'll be honest, I feel deflated. It makes you feel low. It's a disgusting, mindless act which ruins things for everyone else.
"We are trying to make Newport a club that is open for everyone.
"It's a beautiful club, with one of the best views around, and it's tough to see things like this happen with all the hard work the volunteers and coaches put in.
"We are having to work to roll out the pitch again because we have a game on Friday night."
The club is now trawling CCTV in order to provide police with more information.
But Andy said they may also have to look at further security measures.
"We have got to take charge of this because it's just not on," he said. "And that means we might have to put gates up to stop people coming onto the ground because it's private but does have a public right of way.
"It would be a shame because that would take it away from people who behave properly and just take, for example, their dogs up for a walk.
"We don't want to be putting gates across but we might have to.
"We are a club that has progressed and are performing at national levels now.
"We don't need these kind of incidents – with the added costs – hitting us as a club to be honest."