It comes after a “small number” of patients and staff tested positive for the virus.
Stockport NHS Foundation Trust said widespread testing was underway to “control the spread of infection” at the hospital.
In a statement provided to the Guardian, a spokesperson for the trust said: “We have started a rapid screening process for Covid-19 for staff to strengthen our efforts to prevent and control the spread of infection to the Stepping Hill Hospital.
“The changes to lockdown arrangements in parts of northern England reflect the prevalence of infection in our local communities, and we have recently identified a small number of infections among staff and patients.
“We have taken swift action to protect ourselves and those who need our care.
“Friday evening we started the rapid testing program which over the next five days will see all of our hospital staff tested.
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“Infected personnel should self-isolate according to national guidelines.”
The most recent figures for the coronavirus infection rate revealed that cases were on the rise in Stockport during the week ending July 29.
The infection rate continues to climb in the borough, with 61 cases in the same week – the highest number since May 27.
There are 20.9 cases per 100,000 inhabitants in Stockport, up from 8.2 on July 22. The rate jumped 4.1 in just two days.
Targeted lockdown measures were implemented in Greater Manchester on Thursday at midnight, following a worrying increase in the infection rate.
Residents of Greater Manchester have been banned from meeting inside their homes or in gardens.