Wiltshire Police declared a major incident after a man in his 40s and a woman in her 30s became ill at Prezzo in High Street on Sunday evening.
Nearby streets were cordoned off "due to recent events" in the city, but restrictions have now been lifted, the BBC reported.
Police say they are no longer treating the illness as a major incident.
Salisbury is in south-west England where former Russian double agent Sergei Skripal and his daughter Yulia had suffered a Novichok nerve agent poisoning in March.
"Due to recent events in the city and concerns that the pair had been exposed to an unknown substance, a highly precautionary approach was taken by all emergency services," A Wiltshire Police statement said.
In June, two Amesbury residents also fell ill after being exposed to the same nerve agent. Dawn Sturgess, 44, died and a murder inquiry was launched.
The UK government has accused two Russian men, Alexander Petrov and Ruslan Boshirov, of attempting to kill the Skripals.
Last week, the duo told Russian government backed RT channel that they travelled to Salisbury to see tourist sites such as Stonehenge, which is about 16 kilometres from Salisbury.
Russia has denied any involvement in the poisoning incidents.