Tests were being carried out yesterday on a 28-year-old man whose unknown illness sparked a security alert at a hospital, police said.
The patient at Stafford General Hospital was with four men whose "suspicious behaviour" prompted staff to raise the alarm.
Armed officers swooped on a car park at 9.45pm on Wednesday and arrested four men under the Terrorism Act.
The 28-year-old, whose condition staff were concerned about, was moved to another hospital for treatment.
Staffordshire Police said there was no evidence of a terrorist incident or a threat to the area and said anti-terror legislation had been used to detain the men so officers could investigate "a complex set of circumstances".
In a statement, a force spokesman said: "We were contacted by staff at the hospital who developed concerns about the 28-year-old who had been taken there for treatment yesterday afternoon.
"There were concerns about the nature of his illness and what they felt was the suspicious behaviour of four men with him."
The spokesman continued: "Staffordshire Police are now investigating the full train of events to try to understand exactly what has happened. We do not yet know the precise nature of these events. At this stage, there is no evidence that a terrorist incident has taken place nor that there is any specific threat to the area.
"The arrests were made under the Terrorism Act. This legislation affords us the opportunity of investigating what at this stage appears to be a complex set of circumstances."
The spokesman said officers were liaising with the Metropolitan Police Service and Buckingham Palace about the Queen's visit to the town today.
Martin Yeates, chief executive of the Mid Staffordshire General Hospitals Trust, praised staff for their vigilance. He said access to the hospital had been restricted for a short period but that services had been operating normally yesterday.
Mr Yeates said: "I would like to take this opportunity of thanking all the staff involved in the incident for their vigilance and professionalism.
"This is a very sensitive police investigation and therefore we cannot comment further at this stage."
The four men - aged 24, 26, 27 and 30 - from Stafford, remained in police custody last night. ..SUPL: