It is understood the penalty was issued after the man went out socialising in Enniskillen at the weekend.
The man, who later tested positive for Covid-19, was supposed to be self-isolating having recently returned from Spain’s Balearic islands.
People returning from countries that are not on Northern Ireland’s green list for safe travel, such as Spain, are required to quarantine for two weeks.
Details of the incident in Enniskillen were first reported by the Belfast Telegraph on Thursday.
PSNI Assistant Chief Constable Alan Todd confirmed the £1,000 fine was issued on Tuesday.
“The management of the Health Protection (Coronavirus, International Travel) Regulations (Northern Ireland) 2020, is a matter for UK Border Force and their associated partners,” he added.
“The police role is to respond to reports from the UK Border Force or any of their associated partners of potential breaches but police will also act on any significant concerns raised by members of the public.
“As always, our approach remains to engage, explain and encourage, and only where necessary enforce.
“Everyone needs to continue to follow the Government’s guidance to help suppress the transmission of the virus and support our NHS.
“It is encouraging to see that to date there has been a high level of compliance since the introduction of the mandatory quarantine on travellers coming into Northern Ireland from restricted countries and I hope that continues.”