The unnamed 32-year-old was said to be acting "aggressively, raging and threatening" when he was discovered at around 10am on Monday ahead of the crunch match in the city.
A spokeswoman for the Ministry of Interior said no cause of death has been identified.
She told the PA news agency: "A 32-year-old man has sadly died.
"At 10am today, the police received a signal to attend a man in a helpless condition, in the city centre.
"He was a foreign national, from Britain, and he was taken to hospital but he sadly died.
"Police are working to clarify all the circumstances in the incident.
"There is no further detail on any injuries.
"There will be a forensic examination to find out what the cause of death was."
A statement on the authority's website added that in hospital, the victim "suddenly began to act aggressively, raging and threatening".
A Foreign Office statement added: "We are supporting the family of a British man who died following an incident in Sofia, and our staff are in contact with the UK and Bulgarian authorities."
It came as England prepare to take on Bulgaria in Sofia on Monday night.
England supporters were involved in violent clashes with police in Prague on Friday, ahead of the Three Lions' 2-1 defeat to the Czech Republic.
Asked about the trouble after the defeat, England manager Gareth Southgate said: "Of course, always disappointing and I think I've always spoken about how we would want everybody to conduct themselves."