Forecasters predict the region could see half a month’s worth of rain in less than a day.
An amber alert has been issued by the Met Office for counties Antrim, Down and Armagh between 11pm on Sunday and 8am on Monday.
Tonight there were reports that parts of Fermanagh had been deluged, with two roads impassable.
The PSNI said: “Road users are advised the Marble Arch Road, Florencecourt and Sligo Road, Enniskillen are both impassable due to floods this evening.
“Flooding is also affecting other parts of west Fermanagh – please take care when travelling, slow down, and exercise caution on affected roads.”
The expected rainfall carries a risk of flooding, power cuts and dangerous driving conditions.
Forecasters also warned there is a small chance that some communities could be cut off by flooded roads while fast-flowing or deep floodwater could pose a danger to life.
Simon Partridge, a forecaster with the UK Met Office, said: “It looks like Northern Ireland is the place where we could see the most rainfall and certainly the most impactful rainfall.
“They could see 50 to 75mm of rain within 12 to 18 hours.”
The rain carries a risk of localised flooding (Liam McBurney/PA)
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The region records an average of 89mm of rain in July, meaning more than half a month’s rainfall could hit Northern Ireland in less than a day.
The forecaster said: “A spell of very heavy rain is expected to affect parts of east and southeast Northern Ireland during Sunday night and at first on Monday morning.
“There remains some uncertainty in the northern extent of the heaviest rain, but some places are likely to have 50-75 mm of rain in a short space of time with a risk of flash flooding.”
There have already been two separate yellow alerts in place for parts of Northern Ireland, with thunderstorms, lightning strikes and hail all deemed possible.
One alert for counties Fermanagh, Londonderry and Tyrone ran from 12pm until 8pm on Sunday, while the other alert covering counties Antrim, Down and Armagh has been running from 6pm on Sunday and will last until 6pm on Monday.
Amid the more serious amber alert, the Met Office is advising the public to take steps to stay safe, including avoiding travelling if possible and exercising caution around any floodwater.