The "intense" fire destroyed three sheds at premises in Bessbrook, Co Armagh, near the border with the Republic.
The Northern Ireland Fire and Rescue Service (NIFRS) said: "Three sheds were totally destroyed in the blaze and unfortunately 800 sows and approximately 3,500 piglets died in the incident."
The blaze happened at Derrywilligan Road on Saturday.
Firefighters were called to the site at about 5.40am, and it took crews seven hours to bring the situation under control.
Five fire appliances were called as well as water tankers and a hydraulic platform.
Stormont Assembly member Danny Kennedy, who lives a short distance from the farm, said he was shocked.
"This is a very distressing incident. Not only for the loss of this number of animals, but also the impact on this local business."
A Police Service of Northern Ireland (PSNI) spokesman said it was reported that a fire had started at farm premises in the area.
"A number of animals were evacuated from the scene, but it is believed that a number of pigs perished during the incident. It is believed that extensive damage was caused to the property and diversions were in place to minimise traffic disruption.
"At this stage, the cause of the fire is still under investigation and inquiries are continuing."
The force could not confirm exact figures for the number of animals affected.