He was detained at a block of flats in the capital, Guatemala City. His lawyer said he would not fight the extradition request.
"He will prove his innocence in the courts of the United States," said his lawyer, Francisco Garcia Gudiel.
`Six-digit bribe`
Mr Jimenez was head of the Guatemalan Football Federation (Fedefut) from 2010 until last year.
US prosecutors say he and former Fedefut Secretary-General Hector Trujillo took a "six-digit bribe" to sell the television rights to qualifying matches for the 2018 World Cup.
Mr Trujillo was arrested in the US last month.
The US has now charged some 40 individuals and entities as part of the Fifa investigation.
The Department of Justice said it had asked for the arrests because the alleged offences were "agreed and prepared in the United States" and payments were also processed via American banks.
The first charges, against 14 Fifa executives and associates, were brought in May. Some people have already been convicted.
Many others were indicted in the following months.
On 3 December, US prosecutors announced new charges focusing on corruption at the South American Football Confederation and Concacaf, which governs the game in North and Central America as well as the Caribbean.
The football executives were accused of receiving bribes worth millions of dollars connected to Copa America tournaments.
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