Zorislav Srebric, the general secretary of the federation, was held at WH Smith, in Gatwick airport's south terminal, after allegedly stealing stationery.
Officers arrested the 67-year-old in front of the Croatian players shortly after he had arrived at the airport, but he was later released without charge.
A Sussex police spokesman said: "A 67-year-old man was arrested on suspicion of theft from WH Smith at Gatwick Airport's south terminal. He was later released without charge, and no further action will be taken."
Today, officials at the CFF insisted there had been a "misunderstanding". Vlatka Jandel, a spokeswoman for the Zagreb-based federation, said the allegation of theft had not been true.
"I cannot imagine him [Srebric] stealing anything," she said. "Mr Srebric is quoted in Croatian media today as saying there was a misunderstanding, and that this accusation is not true."
In a statement, the CFF said the incident arose when Srebic noticed his team enter the airport building as he was buying newspapers. As he hurried to organise them through airport control, police thought he was trying to avoid paying for the papers, the CFF statement added.
The CFF said: "Unfortunately, he was taken to a police station where they determined that it was a misunderstanding, but instead of five minutes he should stay for a while because of procedure."
England play Croatia tonight in a final Group E game that is crucial to the home side's hopes of qualifying for Euro 2008. The Croats, the current group leaders, have already qualified, but Steve McClaren's team need at least a draw in order to go through.
They were thrown a lifeline when Israel beat Russia at home on Saturday, meaning just one point tonight will ensure England go through ahead of the Russians, who travel to Andorra. If England lose, Russia will take the second qualification spot with a win.
The incident involving Srebric has echoes of the arrest of the then England football captain Bobby Moore in 1970.
Moore was charged with stealing an emerald bracelet in Colombia, though he was later cleared. It was thought the star had been the victim of a blackmail plot.
