Russian-born Anna Shapiro, 30, and her husband Alex King, 42, tested negative for any nerve agent after falling ill at a Prezzo restaurant in the Wiltshire city.
“Both patients are now medically fit and there is no need for them to be in hospital,” said Lorna Wilkinson, director of nursing at Salisbury District Hospital.
“While this incident did not involve nerve agents, it was still clearly very stressful for our staff who, once again, demonstrated the very best of the NHS.”
Police and emergency services, some wearing protective suits, went to the scene on Sunday evening after a major incident was reported at the chain restaurant.
Wiltshire Police said they were assessed at Salisbury District Hospital due to concerns they had been “exposed to an unknown substance”.
Ms Shapiro said she grew concerned when her husband did not return from the toilet after 15 minutes.
“I headed up and saw him lying on the floor near the sinks,” she told The Sun.
“I ran downstairs for help. I was panicked.”
Soon after Ms Shapiro went to raise the alarm, she began to feel unwell too.
Emergency services were called to the city centre restaurant at 6.45pm and the pair were taken to Salisbury District Hospital.
Wiltshire Police said there were no suspicious circumstances.
The restaurant, on Salisbury’s high street, is a short walk from Zizzi, where former Russian spy Sergei Skripal and his daughter Yulia ate before they were found slumped on a bench in the Wiltshire city in March.
The two spent months recovering in hospital from that attack which Theresa May, backed by several Western countries, said was carried out by Russian agents with nerve agent novichok.
The restaurant is also located to the nearby Queen Elizabeth Gardens, which was until recently closed off after 44-year-old Dawn Sturgess was fatally poisoned by novichok in June.