The 11 reception class children, aged between four and five, from Halam Primary School in Nottinghamshire, suffered with “bumps and bruises” on the school trip to Hills Farm, Carvers Hollow, Edingley.
They were “thrown around” when the trailer they were in became detached from the tractor pulling it on March 11.
A female teaching assistant went to hospital with a broken wrist and three others - including a child - were treated in hospital with minor injuries.
Paul Nolan, acting head teacher at the school, apologised for the “unfortunate incident”.
He said: “We wish the children and adults who were injured a speedy recovery.
“We have been in regular communication with everyone affected.
“This incident has affected the whole community and everyone is supporting each other as a result.”
Nottinghamshire County Council said the incident took place in an established trip for reception pupils and that all the appropriate procedures were carried out.
Marion Clay, acting service director for education standards at the council, said: “Parents of children on the trip were notified immediately of the incident as was the health and safety team at the county council.
“We wish those who were injured in the incident a quick recovery and the head teacher will ensure that parents and carers continue to be updated over the coming days.”
Nottinghamshire Police are investigating the incident, with “specialist support” from the Health and Safety Executive.
Anyone with any information should call police on 101, quoting incident 261 of 11 March 2016, or contact Crimestoppers anonymously on 0800 555 111.
The farm is yet to respond with a comment.