The warning was issued on Facebook after a number of people went to the James Cook University Hospital with stomach aches caused by overindulgence.
The post said patients should "rest at home and drink plenty of water" if they had eaten too much chocolate and a big dinner.
It comes as the NHS revealed A&E delays in England had reached record levels.
The data for January from NHS England showed 88.7% of patients were dealt with in four hours - the worst monthly performance since the target of 95% began in 2004.
On Facebook, South Tees Trust NHS Foundation Trust said: "Believe it or not, we do have people coming into A&E with stomach aches caused by overindulgence.
"If you've had one too many Easter eggs and a big Sunday dinner, you're likely to feel better after a rest at home and drinking plenty of water."
In another post, it added: "Earwax, stomach problems caused by overeating, false nails that won't come off, headache, period pain, colds and flu, sickness and diarrhoea - we have seen all of these in A&E in recent weeks.
"Please only attend A&E if you are seriously ill or injured. If you attend with a minor illness or injury, you could face a long wait."
Last week, Peterborough City Hospital's A&E reached "unprecedented numbers" as people with broken fingernails and hiccups turned up for treatment.
People who eat "one too many" Easter eggs have been urged to stay away from A&E by NHS bosses in Middlesbrough.