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."

International development minister Alasdair Allan claimed Brexit will cause "immeasurable harm" to Scotland.
He said further damage could be inflicted by limiting the number of people who can come to the UK.
The UK government said the immigration system takes Scotland's needs into account.
The Scottish government has vowed to oppose any changes to the rules which create barriers for businesses by preventing them from taking on the staff they need.
The number of people living in Scotland is projected to grow by 7% between 2014 and 2039, with 90% of the rise in the next decade expected to come from inward migration.
In a letter to the UK Home Affairs Select Committee's inquiry into immigration policy, Mr Allan said a "key priority" in tackling Scotland's ageing population was attracting working-age migrants to the country.
He said: "That is why we need the UK government to deliver an immigration system that meets Scotland's needs - because we depend heavily on new Scots to support our economy and communities.
"However, net migration targets and caps are too blunt an instrument to address the complex needs of our economy.
"The UK government's focus on arbitrarily reducing net migration figures, irrespective of the value migrants bring, what skills shortages they could address or what contribution they could make, is wrong for Scotland and is harming our economic prospects."
The UK government has already rejected a call to consider devolving immigration powers to Scotland and changing visa arrangements to encourage students from other countries to stay on north of the border after graduating.
A Scottish Affairs Committee report recommended UK ministers consider "sub-national migration powers" for Scotland and a tailored post-study work scheme.
The UK government response, published on Friday, stated it "does not intend to reintroduce a general post-study work scheme for Scotland" and stressed the immigration system is "designed for the whole of the UK" but takes Scotland's needs into account.
Officers are facing disciplinary action over claims a prisoner had sex during a hospital visit, the BBC has learned.
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Any moves by the UK government to limit immigration could "seriously harm" Scotland's economy, a Holyrood minister has warned.