The 71-year-old man sustained serious bruising and injuries to his arms, legs and head.
Nottingham Crown Court was told that the employee was operating a tractor fitted with a mounted grab attachment to collect branches for burning.
The disabled man was on a guided walk in the park. The council worker did not see him and ran into him.
The Health and Safety Executive (HSE) found the council had not given its workers sufficient training to safely operate mounted grabs or act as banksmen. It had put its own staff and the public at risk by failing to segregate vehicles and pedestrians, and not adequately planning or supervising the work.
The HSE also said the tractor was unsuitable for transporting the branches long distances.
Nottinghamshire County Council pleaded guilty to breaching ss 2(1) and 3(1) of the Health and Safety at Work Act and must pay £10,270 costs.
HSE inspector Martin Giles said after the hearing that the council's failings had endangered other members of the public walking with the OAP.
Anthony May, chief executive of Nottinghamshire County Council, said: “We know things went very wrong on the day and that we failed in our duty of care. For that reason, we have worked hard to improve health and safety arrangements at Rufford Abbey, and across the council.
"We acted immediately after the incident by having our own internal investigation, as we wanted to find out what had happened and what had gone wrong. We cooperated fully with [HSE’s] investigation, sharing evidence, findings and witness statements from our own investigation. When the HSE brought charges against the council, we did not at any stage contest them.
"While it is of course highly regrettable that this happened in the first place, we have contingency funding to be able to meet this size of fine. When setting and planning our budget we always allow for whole range of risks.
"We have taken action to review and improve the way we do things to make things safer, as we want to reassure people that Rufford Abbey is a safe environment for everyone.
"Since June 2015, we have improved driver training, updated and improved our risk assessments for vehicle use, reviewed and improved our arrangements for managing vehicle movement in the park, improved our public information at the park about vehicle movement, and improved our arrangements for the supervision of employees.
"In light of this incident, we have also taken the opportunity to renew our health and safety focus across the whole council to further make sure that all our public services operate in the safest way they can."