Vandals smashed through security fencing and damaged play equipment waiting to be installed at the play area in Sorrel Drive over the weekend.
Council officers believe an axe or machete was used in the attack.
Vandals targeted the play area again on Wednesday (24 January), damaging a slide.
Work on the play area refurbishment started earlier this month, with plans including new play equipment and landscaping work.
But council officers have spent the week counting the cost of the vandalism and checking whether the damaged equipment and parts can be salvaged.
Cllr Adam Daly, Rugby Borough Council portfolio holder for leisure and wellbeing, said: "These mindless acts of vandalism have caused considerable damage and I'd encourage witnesses or anyone with information to contact the police.
"We worked with the community through public consultations to finalise the design for the refurbishment and I'm sure the vast majority of residents share our frustration and disappointment.
"We're now working with our contractors to calculate the cost of the damage and source replacement equipment and parts, and we still hope to unveil the refurbished play area in the spring."
New play equipment set to be installed at the play area includes a seesaw, roundabout and swing, with play panels designed for younger children to enjoy.
Other play equipment featured in the refurb includes a 'hula' rotator, embankment slide, stepping pod and 'talk tubes', which allow children to communicate with friends and family while playing.
Witnesses or anyone with information about the vandalism at the Sorrel Drive play area should call police on 101.