Sergei Skripal, who is 66, was granted refuge in the UK following a "spy swap" between the US and Russia in 2010.
He and a woman, 33, were found unconscious on a bench at Maltings shopping centre in Salisbury on Sunday afternoon.
The substance has not been identified.
He was convicted of passing the identities of Russian intelligence agents working undercover in Europe to the UK's Secret Intelligence Service, MI6.