The Dutch-registered Annelies Ilena, formerly the Atlantic Dawn and registered in Ireland, was stopped about 100 miles north-west of Tory island off Co Donegal.
The Defence Forces said its ship, the LE Roisin, had made a significant detention for alleged breaches of fishing regulations and detained the boat shortly after 11am this morning. It is expected into Killybegs this evening.
The Annelies Ilena is about 144m or 474ft long and weighs in at about 14,000 tonnes while the LE Roisin weighs in at 1700 tonnes.
Gardai and the Sea Fisheries Protection Authority are involved in the investigation.
The trawler which fishes for pelagic species of fish, such as herring, is the largest boat ever detained by the navy and it is the 13th detained for alleged infringements of fisheries regulations this year.