The Ministry of Justice said a number of prison staff were being investigated.
An HMP Chelmsford inmate's girlfriend told The Sun they were allowed into a shower room at Broomfield Hospital where they had sex.
Chelmsford MP Sir Simon Burns raised concerns about the issue in September and said there should be sackings.
In a letter to Sir Simon, the prisons minister Andrew Selous said a full investigation had been conducted.
"A number of prison officers will be required to attend a disciplinary hearing which will consider the appropriate action that should be taken against them," he said.
"Explicit instructions are also being put in place at the prison that make clear to staff the expected standards of supervision that are required during the time a prisoner is at a hospital.
"I hope this letter has been able to reassure you that, whilst it appears that there was an unfortunate lapse in supervision on this occasion, steps are being taken to robustly address the matter and avoid any such repetition."
Sir Simon said: "It was a very unfortunate incident which was totally unacceptable.
"I welcome the update from the minister and the assurances that measures have been put in place to ensure this does not happen again."
Officers are facing disciplinary action over claims a prisoner had sex during a hospital visit, the BBC has learned.