The BA 747 hit several runway lights after landing
No-one on board the Boeing 747-400 plane was injured after the incident.
BA said the pilot could not see the lights leading to the taxiway - causing him to hit more lights - and the plane had to be realigned.
Mr Blair was on his way to stay with Bee Gees star Robin Gibb at his house in Miami Beach.
The prime minister was seated in first class on flight 209 from London, which landed at 1815 local time (2315 GMT) on Tuesday, the US Secret Service said.
"The captain believed the lighting on the taxiway was not sufficient to guide him and an airport vehicle was requested to realign the plane," a BA spokeswoman said.
'Landed safely'
The plane, which was not damaged, then taxied to the terminal under its own power and passengers disembarked normally, she added
The prime minister and his family are staying with Robin Gibb, the former Bee Gees star, who has a $10m [£5.1m] house here in Miami Beach
Evan Benn, Miami Herald
According to Federal Aviation Administration spokeswoman Laura Brown the plane stopped just past the end of the runway.
"It landed safely on the runway. It slowed down. It was going at taxiway speed and they just missed a turn," she said.
Airport spokesman Marc Henderson said the jet had hit several airfield lights after landing but had not left the concrete surface.
Evan Benn, a reporter for the Miami Herald newspaper, told BBC News Mr Blair was holidaying in Florida.
"The prime minister and his family are staying with Robin Gibb, the former Bee Gees star, who has a $10m [£5.1m] house here in Miami Beach," he said.
Downing Street confirmed Mr Blair was on his winter holidays but said it never commented on specific arrangements.
A British airways flight from London, England to Miami, Florida containing British prime minister Tony Blair has missed a taxiway at Miami airport. The Boeing 747-400 plane hit lights as it was turning off the runway onto a taxiway taxiing at 1815 local time on Tuesday evening (2315 GMT).

The pilot couldn't see the correct taxiway due to poor lighting, said British Airways spokesman John Lampl.

Prime minister Tony Blair, with his family, was on his way to stay with Bee Gees star Robin Gibb at his house in Miami Beach when the incident occurred. The plane and all 343 passengers onboard were not damaged or hurt.

A U.S. safety board has said that it's now investigating the incident.