The DFDS Seaways service from North Shields, Tyneside, was forced to abandon its voyage to Amsterdam on Saturday evening after one man allegedly set fire to his own cabin.
Police have since confirmed a 26-year-old man has been arrested on suspicion of arson after being detained by ferry staff.
A 28-year-old man was also arrested on suspicion of affray, as fighting broke out among passengers.
Among the passengers were a number of Scots on their way to the Netherlands.
One Scottish passenger, identified only as Dawn in a TV report, said: "The fire alarm went off and we were all told to evacuate. We were outside on the deck in the freezing cold for at least 45 minutes.
"The decks were very crowded, there was a lot of people running around, obviously scared. They were petrified.
"There was kids crying and really it was just a bit chaotic, to be honest. It was just awful."
Her son, who was travelling with her, spoke of the disorder that followed the evacuation as a number of people became agitated.
He said tensions had flared among a handful of passengers who were "drunk and disorderly" after revelling in the ferry's nightclub.
One fellow passenger described the scenes as a "chaotic mess", while another said people were simply "going wild" on the deck.
Early indications are that the fire was caused by a smoker in his own cabin; however, the police have yet to confirm the source of the blaze.
Inspector Andrew Dixon from Humberside Police said: "It is unknown if the fire was started deliberately or accidentally."
The two men who were arrested in the early hours of Sunday morning remain in police custody while investigators continue their inquiries.
The cruise ferry was travelling across the North Sea with 946 passengers and 127 crew on board. It was 30 miles off the coast when the fire alarm went off, shortly before 11pm.
A handful of young children were on the deck, many of whom had been whisked from their beds in nightwear and without shoes or socks.
An alert from the ferry crew sparked a major rescue operation as RAF helicopters stationed near Hull were scrambled to the scene.
A total of six people were taken to hospital in Scarborough for treatment but all have now been discharged.
A further 15 passengers and eight crew members were treated by doctors for smoke-related injuries while on board.
The ferry was forced to return to port, where investigators held the ship in dock while conducting door-to-door inquiries.
Some passengers were forced to stay onboard the ferry for as long as five hours as they waited to be questioned by police. "We spend five hours waiting," said Dawn. "It's ridiculous, we weren't informed about anything, really."
Gert Jakobsen, vice-president of DFDS, claimed the company would help arrange alternative crossings for those who were turned back.
He also added that "psychological assistance" would be provided to anyone who needed it.
He said: "We are very sorry for those passengers who have not only been affected by the fire but now by these delays. We are looking at how we can help them.
"The cabin that was burnt is very damaged and there has been some smoke damage to surrounding cabins but the ship's function has not been affected in any way and is safe to travel."