North Yorkshire Police shared the incident on Facebook, just a day after they urged people to stay at home during the lockdown.
A spokesman said: "Yesterday we issued fines to two people from West Yorkshire found camping and having a BBQ near Helmsley.
"Usually we welcome visitors to North Yorkshire with open arms. However, for the sake of our region and the nation, please stay home and save lives."
More than 350 fixed penalty notices have been issued since the legislation was introduced in March and nearly half of those have been issued to non-residents who are coming into North Yorkshire, to visit an open space or beauty spot.
On Friday, April 25, the force issued a statement after seeing an increase in people make unnecessary trips to the region.
Assistant Chief Constable Mike Walker said: "Usually we welcome visitors to North Yorkshire with open arms. However, for the sake of the health and safety of both the region and the nation, we are asking you to please stay away for the time being.
"We are aware of confusion that has arisen over the guidance around travelling for exercise and can understand that many people are looking for clarity around this issue.
"I believe the guidance issued by the UK Government couldn’t be clearer – to stop the spread of this potentially lethal virus, to protect the most vulnerable in our communities, our loved ones and our health service – we must all stay at home.
“In short, the virus moves if people move.
"So the way to stop the spread is to limit our movements down to only the very essential. I do not believe a group of friends travelling from West Yorkshire to climb the Yorkshire Three Peaks is essential nor do I believe a group of people travelling into the Yorkshire Dales from Bradford for a day out is essential.
"Exercise can be and should be taken locally following the Government guidelines, which have not changed since the day they were issued.
He added: "Please believe me, I understand how important exercise is to people’s mental health.
"However, exercise can be taken from your doorstep and there is no reasonable or justifiable need to make a 50-mile trip to the coast, putting your own safety and the safety of others at risk.
"If we continue to stay home, this will be over all the sooner."
Chair of North Yorkshire Local Resilience Forum, Richard Flinton, said: "For those who still think a drive into our countryside is just the ticket on a warm spring day then our message is very clear.
"If you flout the national lockdown rules you may receive the ticket you didn’t want – by way of a fine.
"We are working really hard to educate people, but ultimately you risk a penalty and we are looking at further visibility along key routes, to drive the message home to the minority who aren’t sticking to the rules.
"Because the sun is up it doesn’t mean the virus is not every bit as deadly.
"Anyone can carry it, anyone can spread it and it is indiscriminate in who it hits hardest."