The new measures come in force from today, Thursday 29 December.
Patients and visitors are also being asked to wear a mask in order to prevent the spread of infections to vulnerable patients, as well as to help prevent staff absences.
Visiting will be restricted to compassionate visiting only for adult wards, which can be discussed on an individual basis with the ward team.
However, there will be increased virtual visiting offered, to support patients to keep in touch with loved ones.
Maternity, paediatrics and patients who need compassionate visiting will not be affected.
It comes as they have seen increased numbers of people in hospital with Covid and flu., with some patients seriously ill with both illnesses simultaneously.
The Trust says in September Covid infections had dropped to as-low-as 16 beds occupied across the two hospitals.
However, the new measures come after that combined figure yesterday has risen to 120 beds occupied with Covid across the two hospitals.
In addition to this, the Trust says it is facing additional pressure from flu cases. Across the two hospitals there are currently more than 70 beds taken up with flu.
In a joint statement, Northampton and Kettering General Hospital’s Chief Operating Officers Palmer Winstanley and Fay Gordon said: "The UK is now experiencing a significant spike in winter illnesses including Covid, flu, RSV and norovirus. The current variants are very infectious, and we are seeing numbers rise in both hospitals with some patients being very unwell.
"As a result, we are suspending visiting on adult inpatient wards and are asking all patients and visitors to wear masks when coming to the hospital. This will help us to prevent the spread of infection and keep our vulnerable patients safe from these winter illnesses.
"As well as this we would ask anyone needing to come to the hospital to wash or gel their hands to support good hand hygiene.
"We are also urging people to have their Covid and flu vaccinations. We are seeing patients who are being hospitalised with both flu and Covid and a number of these patients are seriously unwell and unvaccinated."
This guidance will be reviewed continuously, and the hospital will provide regular updates via their website and in local media.