The damage was discovered on Monday morning – and the borough council has now appealed for the public’s help to catch the culprit.
A £100,000 revamp of the recreation ground took place in 2014, with the outdoor gym equipment being added to the park’s attractions.
But the recumbent bike was badly damaged in the crash and, with the car park barrier also in need of replacing, the council fears the final repair bill could top £3,000.
Cllr Lisa Parker urged anyone with information about the incident, which the council thinks took place over the weekend, to contact police.
“Whether accidental or malicious, the person responsible for this damage had a duty to report it,” Cllr Parker said.
“We now face a hefty repair bill, money which could be better spent on making further improvements to our borough’s parks and green spaces.
“The number of residents who took part in our consultation to help design the park’s revamp showed how much the community values Alwyn Road Recreation Ground, and I’d encourage anyone with information about the incident to report it to the police.”
Information can be reported to Warwickshire Police by calling 101, quoting incident number 130 of 1 March.