Police were called to Haven Caravan Park in Low Road on Monday afternoon, following reports of two people being injured.
After the quick arrival of officers, it was discovered that a dog had injured the two victims, who had to go to hospital for treatment.
Essex Police has confirmed that a 28-year-old man from Harwich has been arrested following the incident.
He has since been released on bail while inquiries continue.
The dog was put to sleep following the incident.
Its owner said it was a “much-loved family dog” and the incident was “completely out of character”.
They confirmed the dog was put to sleep by a vet at their property, leaving the family “gutted”.
Tendring district commander Chief Insp Ella Latham said: “We are continuing an investigation after two people suffered serious injuries in an incident involving a dog in Dovercourt.
“We were called to Haven Caravan Park, in Low Road, at around 1.30pm on Monday, January 6.
“It was reported a dog was dangerously out of control and two people had been injured.
“Officers arrived at the scene within minutes.
“Their professionalism ensured the dog was secured and the threat to the public was minimised.
“I would thank the officers who dealt with this incident and the veterinary professionals who bravely worked with us at the scene.
“A man and a woman were taken on to hospital with serious arm injuries.
“A 28-year-old man, from Harwich, was arrested on suspicion of being in charge of a dog dangerously out of control causing injury.
“He has since been released under investigation while our enquiries continue.
“Anyone with information should contact us as soon as possible and I would urge anyone in the community with concerns to reach out to us.
“Please cite reference 42/2448/25.”
The police can be contacted using the online Live Chat service, at essex.police.uk or by calling 101.