A major incident was declared on Sunday when a man in his 40s and a woman in her 30s became unwell at a Prezzo restaurant in the city.
Roads were cordoned off and police and paramedics wearing protective suits were deployed in the area amid heightened tensions following the deadly Novichok attack.
Wiltshire Police said that, due to recent events in the city and concerns the pair had been exposed to an unknown substance, a "highly precautionary approach" had been taken by emergency services.
The force said in a statement: "Both were taken to Salisbury District Hospital and were clinically assessed. We can now confirm that there is nothing to suggest that Novichok is the substance. Both people remain in hospital under observation.
"The major incident status has now been stood down."
Investigators were trying to establish if the pair had been victims of a crime and the restaurant remained cordoned off on Monday morning.
Police were called to the Italian restaurant on the corner of High Street and Crane Street by the South Western Ambulance Service at around 6.45pm.
A source briefed by the emergency services told the Press Association: "The ambulance crew at the site took the decision that the symptoms seemed consistent with Novichok poisoning which is why they called their colleagues in the police."
But the source stressed: "The symptoms of Novhichok poisoning and particular types of narcotic abuse are very similar."
Four ambulances including a hazardous area response team were sent to the restaurant, while Public Health England was also informed.
Witness Sam Proudfoot, 16, said he saw a person in a hazardous material suit go between the restaurant and the ambulance.
The Italian restaurant is a short walk from Queen Elizabeth Gardens, which was until recently closed off after 44-year-old Dawn Sturgess was fatally poisoned by the nerve agent in June.
Also nearby is Zizzi, the Italian restaurant where former spy Sergei Skripal and his daughter Yulia visited before they were taken ill in March.
Police said Ms Sturgess was killed by the same chemical used in an alleged hit by Russian military intelligence officers on Mr Skripal.
Salisbury City Council leader Matthew Dean tweeted: "Understandably people concerned at latest possible incident in Salisbury but there have been a number of false alarms since the Skripal poisoning.
"Rightly the emergency services start with a highly precautionary approach until they know otherwise."
Salisbury District Hospital remained open during the incident.
Cara Charles-Barks, chief executive of Salisbury NHS Foundation Trust, said staff had done an "amazing job".
"Immensely proud of our teams here at Salisbury #OutstandingEveryTime," she tweeted.