Residents will not be able to register at the surgery until Wednesday, September 28, after the decision was made to "protect its patient services".
The centre came under fire recently as patients claimed that it was difficult to use its telephone system and that there were not enough appointments available.
However, Bedfordshire, Luton & Milton Keynes Clinical Commissioning Group (BLMK CCG) - now the Bedfordshire, Luton & Milton Keynes Integrated Care Board (BLMK ICB) - said that a new phone system was being installed to help improve the situation, and that patients would be "offered an appointment with the most appropriate member of the primary care team based on their need".
Commenting on its website, the Ivel Medical Centre said: "In order to protect our patient services we have recently applied to Bedfordshire, Luton & Milton Keynes Clinical Commissioning Group (BLMK CCG) with an application to close our list to new patients.
"We have now had confirmation that our application has been approved by the Primary Care Commissioning Committee.
"Whilst our list is closed, we are only permitted to accept an application for inclusion on our list from a person who is an immediate family member of a currently registered patient and lives in the same household – there are no exceptions to this rule."
Its list, which closed on June 28, will re-open on September 28 – however, the closure may be subject to extension if required by the centre and approved by the CCG.
The centre added: "We apologise for any inconvenience caused".
A spokesman from the BLMK ICB said: “Sometimes a General Practice may wish to close its list temporarily to new registrations, for example where there are internal capacity issues, premises refurbishment or exceptional workforce pressures. In such situations, however, they can continue to register new babies and family members of existing registered patients
“In advance of approving such an application, there is a rigorous process that includes consulting with neighbouring practices and presenting the application to a Primary Care Committee who will assess the application in a complete and rounded approach.
"The committee is chaired by a lay member and includes Healthwatch representatives, as well as experienced GPs.”
The spokesman added: “Between them, they always consider what is best for the patients of the area in the longer term.”