The England fan was killed in Lisbon's central Baixa business district, a police spokesman said.
The attack was unrelated to rivalries in the European soccer Championship being held in Portugal, he added.
"There was an attempted robbery, which led to the aggression against the English fan," he said.
"This had nothing to do with Euro 2004."
UK media cited Portuguese police as first saying a Croatian man had been arrested in connection with the incident, then correcting that to say he was Ukrainian.
"At the moment all we can do is confirm that a British fan has been stabbed to death in Lisbon," a spokesman for Britain's Foreign Office said in London.
"It happened in the early hours of the morning."
England beat Croatia 4-2 on Monday night to reach the quarter-finals of the Euro 2004 tournament.
The British spokesman said the name of the victim was being withheld until next of kin had been informed.
-- Additional reporting by Jeremy Lovell in London
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