Irish setter Jagger died after the event in Birmingham earlier this month, having allegedly eaten beef laced with poison.
A post-mortem examination found two "fast-acting" poisons in the meat but Jagger showed no signs of illness until he was back in Belgium, the club said.
It said it was "inconceivable" the dog was poisoned at Crufts.
Jagger, who came second in his class at Birmingham's NEC on Thursday, is owned by Belgian Aleksandra Lauwers and Leicester-based breeder Dee Milligan-Bott and her husband, Jeremy Bott.
His Leicester-based co-owners declined to comment when contacted by the BBC.
They have previously said he must have been poisoned "while on his bench" at the show at the National Exhibition Centre (NEC).
Three-year-old Jagger, whose pedigree name is Thendara Satisfaction, died on 7 March after returning to Belgium with fellow owner Aleksandra Lauwers.
A spokesman for the Kennel Club said: "There has been a lot of concern about whether the poisoning happened at Crufts and we are now able to reassure all dog lovers who came to Crufts that this could not have been possible.
The spokesman added it was "highly likely that the poisons, thought to be on a piece of beef, were eaten in Belgium, shortly before Jagger's death".
Severe symptoms from the two poisons - carbofuran and aldicarb, which are banned in the EU - would usually occur within 30 minutes to three hours, the club said.
The spokesman said that because Jagger showed the first clinical signs associated with the poisons shortly before his death in Belgium, "we must conclude that it is inconceivable that he could have been poisoned at Crufts on Thursday 5 March, some 28 to 36 hours earlier".
"Furthermore, the poison is thought to have been given on a piece of beef that was still largely undigested when the autopsy was performed on Saturday 7 March morning, and food is usually absorbed in dogs within six hours," he added.
Speaking at the time of Jagger's death, co-owner Jeremy Bott said he did not think the dog was specifically targeted, but the culprit may have been acting on "a grudge against dogs or the Crufts show".
Days after the dog's death, The Telegraph published claims from other exhibitors stating their dogs were sick after the event but Crufts said it could not look into the claims as it had "no direct information".
There were also claims another dog - a shih tzu - was fatally poisoned, but the club said it had not received any information about it and confirmed no shih tzus were seen by vets at the show.
The club said on Monday: "We have a lot of security measures in place to protect the dogs at our show and we continually review our procedures because the welfare and safety of the dogs is our first and main priority.
"Regardless of the fact that the poison was not ingested at Crufts a dog has very sadly died and we must now respect the owners' privacy and give them time to grieve."
A dog who died after competing at Crufts appears to have ingested poison in Belgium, the Kennel Club has said.