Kevin McGeever was emaciated and disorientated when found wandering barefoot on the side of the road near the Cavan-Leitrim border on 29 January this year.
The 68-year-old former tycoon was arrested at his Craughwell home in Co Galway on Thursday and held under section four of the Criminal Justice Act 1994, which contains provisions for wasting police time and making false allegations.
McGeever, who is from Swinford, Co Mayo, had a long beard, hair and nails and was treated for malnutrition when he was found by a motorist.
He had lost about five stone and claimed he was abducted at gunpoint from his gated mansion on 17 May last year. He had been reported missing by his partner last June.
A Garda Siochana spokesman confirmed a 68-year-old man had been arrested in relation to the ongoing investigation into the abduction.