Jimenez, 61, was detained in an apartment in a posh suburb of Guatemala City yesterday, the head of the national civil police force Nery Ramos told reporters.
As well as being president of the Guatemalan soccer federation, Jimenez was a member of the FIFA committee for fair play and social responsibility.
Ramos said Jimenez "was in a bad physical state" having been on the run since December 3 when US courts issued a warrant for his extradition.
They are suspected of taking bribes to grant marketing rights for major FIFA fixtures, violating US laws on wire fraud, racketeering and money laundering.
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Another Guatemalan, the federation's former secretary general Hector Trujillo, 62, was arrested in Florida last month. He was freed on bail last week.
The Guatemalan courts must now decide whether to extradite Jimenez.
The scandal over allegations of multimillion-dollar bribes has led to the suspension of numerous other top officials including Sepp Blatter, longtime president of FIFA.