The “devastating incident” occurred when someone using a bridleway on farmland near Wykeham deliberately tied and propped two gates open.
The sheep then strayed into neighbouring woodland where they were poisoned, and later died.
It is believed the sheep could have eaten ivy or rhododendron which would have killed them.
Following their deaths, farm manager Mike Cleasby has made a bold appeal for people to be more responsible when out in the countryside.
He has put a picture of the dead sheep and a notice on the gate warning of the consequences of leaving gates open.
Mr Cleasby, who looks after the sheep at East Moor Farm during the winter for another farmer, said: “To deliberately tie open a gate in a field where livestock are kept just beggars belief.
“Not only am I out of pocket for the sheep but I’ve also had to pay to get them taken away and disposed of.
“This is a case of the good old farmer paying once more for someone’s carelessness.
“It is just devastating.”
Mr Cleasy said the sheep are Swaledales, a breed which saw one sheep recently sell for £28,000.
He added: “This farmer has spent his life building up this flock for someone to come along and do this. Its beyond belief.
“We had the sheep valued at £2,500 but they could have gone on to fetch more.”
Both gates had been fitted with self-closing mechanisms, however the perpetrator had used string to tie one open while the other was propped so the sheep could escape.
As a result of the incident, and in light of lambing season getting underway, the North York Moors National Park Authority is reminding people to act responsibly by leaving gates as they find, keeping dogs on leads, and taking note of livestock warning signs on the roads.
Jay Marrison, the National Park Authority’s southern area ranger, added: “We want people to enjoy the North York Moors but they do need to be mindful that it is a working landscape and actions such as propping gates open can affect others’ livelihoods.
“The stunning scenery and extensive network of tracks and trails don’t happen by chance and farmers and landowners play a big part in looking after the National Park.
“We would urge people to follow the Countryside Code when out and about in the North York Moors.”
More information about the countryside code can be found at the Natural England