Fire crews were able to protect apartments on two sides of the vehicle park, the hotels and the Arena building, as well as assisting with the evacuation of the horses.
Authorities said that no one was believed to have been seriously injured.
"We are likely to be engaged at the scene for several hours and further investigation will follow firefighting action", Merseyside Fire and Rescue Service said in an update Monday.
The blaze consumed a multi-storey auto park close to The Echo Arena where the prestigious event was due to take place. "We just grabbed the keys and ran".
According to witnesses, vehicles appeared to explode every couple of seconds during the time when the blaze was at its peak.
Horses which were on the first level of the vehicle park when the fire broke out were moved into the arena.
"If it had started 15 or 20 minutes later, we would all have been in our cars trying to get out of the multi-storey".
Five minutes later, everyone was told to "basically get out" because of a fire in the multi-storey vehicle park, she said. "I think that's a very good outcome indeed".
Anyone who has been affected by the fire at Liverpool Echo Arena and are unable to get home or need temporary shelter, Liverpool City Council has opened a Reception Centre at Lifestyles, Park Road, Steble Street, L8 6QH.
Sunday's evening session was the final event in the horse show.
She described how the horses were brought into the arena to keep them safe, including some that had been safely removed from the ground floor of the auto park.
They added: "Thank you for your patience and cooperation while emergency services continue to deal with this incident".