"We can now confirm that there is nothing to suggest that Novichok is the substance.
"Both people remain in hospital under observation."
The police said the major incident status had been stood down.
Some roads remained cordoned off around the Italian restaurant, which 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.
Also nearby is Zizzi, the Italian restaurant where former spy Sergei Skripal and his daughter Yulia visited before they were taken ill.
Pictures from local press showed a hazardous material suit in the area while a police officer was seen in protective clothing with their face covered.
Public Health England was informed of the incident, while firefighters were also at the scene.
Witness Sam Proudfoot, 16, said he saw a person in a hazardous material suit go between the restaurant and the ambulance.
"I've been told two people were taken ill in there," the student said.
"There's a man in a full white body suit with a mask to his mouth going in and out of the back of the ambulance and the restaurant.
"The police were interviewing a couple of dozen people."
Tensions are heightened in the cathedral city because of recent Novichok poisonings.
Britain has said Russian officers used the nerve agent Novichok to attack the Skripals. The Kremlin has denied any involvement.
Police have said a nerve toxin had been left on the front door of the Skripals’ home. They were found slumped in Salisbury city centre after visting the Bishop’s Mill pub and Zizzi, another Italian restaurant.
The former Russian spy and his daughter survived the murder attempt, but Sturgess, unconnected to the duo, died in July and her partner Charlie Rowley fell ill after Rowley found a perfume bottle containing the same nerve agent.
Earlier this month British prosecutors identified two Russians they said were operating under aliases - Alexander Petrov and Ruslan Boshirov - whom they accused of trying to murder the Skripals with a military-grade nerve agent.
Britain charged the two men in absentia with attempted murder, and said the suspects were military intelligence officers almost certainly acting on orders from high up in the Russian state.
Two Russians resembling the men said on television on Thursday that they were innocent tourists who had flown to London for fun and visited the city of Salisbury to see its cathedral.
They surfaced a day after President Vladimir Putin said Russia had located Petrov and Boshirov, but that there was nothing special or criminal about them.