Muslim convert Christoph Martin Häusler was arrested in August 2010 after entering the Russian republic from Finland without a visa, prosecutors said in a statement.
He was serving a 10-month sentence for crossing the border illegally.
Häusler fled the penal colony where he was being held just a few days before the end of his sentence, possibly to avoid extradition back to Switzerland, North Ossetia interior ministry spokeswoman Alla Akhpolova told AFP.
"It's clear he had problems with the Swiss police," she said.
Police have launched a hunt for the convict who has neo-Nazi tattoos on his body, including the letters SS.
Prosecutors said he converted to Islam in Turkey five years ago.