The pub, which is part of the Greene King estate, was sealed off by police shortly after the victims were found unconscious on a bench in nearby The Maltings shopping centre. Police have also cordoned off the nearby Zizzi restaurant.
The victims remain seriously ill and the incident is being treated as attempted murder, police said.
A police officer who was one of the first to attend the scene is also in a serious condition in hospital.
A spokesperson for the Mill said: “We are supporting the police with their investigations. The pub is currently closed, we apologise to our customers for any inconvenience caused.”
'Public safety is a priority'
Counter terrorism police are conducting the investigation but were unable to say how long the Mill or other affected nearby sites would be closed for.
In a statement, Assistant Commissioner Mark Rowley from the Metropolitan Police said: “Public safety remains our priority and this is clearly an awful incident, and I know local people will be concerned but I would stress that at the moment we are not seeing any evidence of a widespread health risk.
“Having established that a nerve agent is the cause of the symptoms leading us to believe this is attempted murder, I can also confirm that the two people who originally became unwell were targeted specifically.
"Our role now is to establish who is behind this and why they carried out the attacks. To that end, we have hundreds of detectives, forensic specialists, analysts and intelligence officers working together around the clock on the case.”
The police said they would not be providing more information at this stage about the nerve agent.
The police are examining hundreds of hours of CCTV footage to build a detailed timeline of events and officers in protective clothing will continue to be visible in central Salisbury as they go about their work.
Assistant Commissioner Mark Rowley said: “I’m sure you understand we need to be both painstaking and thorough to protect public safety and to secure the maximum amount of forensic evidence – indeed the work in Salisbury may take several days."
The police reiterated their call for information from anyone who visited Salisbury town centre or the surrounding areas on Sunday afternoon on 4 March, particularly anyone who was close to the The Maltings shopping centre, anyone that visited Zizzi restaurant and the Mill between 1pm and 4pm.
Any members of the public who have photos or footage that could assist the police should send them to a dedicated website: www.ukpoliceimageappeal.co.uk