John Mallalieu, 89, was in an ambulance near King's Mill Hospital when it was diverted to a unit 14 miles away in Nottingham, his wife Ruth has said.
Mr Mallalieu is now "in a terrible state" in intensive care, she added.
Dr Mark Jefford, from the Newark and Sherwood Clinical Commissioning Group, said he would co-ordinate a thorough investigation into what happened.
Mrs Mallalieu said she was told that a consultant at Kings Mill Hospital, in Sutton in Ashfield, would see her husband as long as he got there by 17:00 GMT on Friday 6 December.
But the ambulance had to turn around and head to Nottingham City Hospital when it appeared they would miss the deadline by a few minutes, she said.
Dr Jefford, the clinical lead of the local commissioning group, said: "I'd like to apologise on behalf of the whole NHS and local health community for the experience that Mr and Mrs Mallalieu have received.
"No matter what the outcome of the investigation clearly it has been a stressful journey and stressful time for the family.
He added: "Clearly in this situation whatever the outcome [of the investigation] we've failed in terms of not providing the best experience for Mr and Mrs Mallalieu."
Sherwood Forest Hospitals NHS Foundation Trust, which runs King's Mill, said its stroke service is run from 08:00 on Monday to 18:00 GMT on a Friday.
It added that it takes about one hour to treat a patient so the agreed cut off time for receiving new patients is 17:00 GMT.
Dr Jefford said he would be drawing together conclusions from investigations by the trust, East Midlands Ambulance Service (EMAS) and the Nottingham University Hospitals NHS Trust.
An NHS official has apologised after a stroke patient was diverted away from a Nottinghamshire hospital.