The Conservative MP made the claim after travelling 0.06 miles, or approximately 96.5 metres, within his North Somerset constituency from a concrete firm to a constituency surgery in Yatton in October 2012.
The Independent Parliamentary Standards Authority (Ipsa) notes the claim was paid last December.
Mr Fox also had another 15 claims of under £1 for car travel approved in 2012/13.
These included 24p for a 0.54-mile journey from a constituency surgery to a school competition in Clevedon and 44p for a 0.98-mile journey from a meet your MP event at Winford Manor to Winford School.
MPs can claim 45p per mile.
Ipsa paperwork shows Mr Fox claimed £3,866.31 in travel expenses in 2012/13, which includes rail fares.
Mr Fox, who worked as a GP before becoming an MP, told the Sunday People: "I don't do my expenses. My office does them. But they are all done according to the rules for travel distances."
The Tory was last year ordered to repay £3,000 of expenses for allowing his friend Adam Werritty to live rent-free at his taxpayer-funded second home for a year.