Alton Towers owner Merlin Entertainments says the rollercoaster accident at the theme park in June could affect profits by up to £47m.
The accident, which resulted in several people being seriously injured, led to the temporary closure of Alton Towers.
Merlin said that the incident had an adverse effect on trading at the start of the important summer period.
Profits for the theme parks division in 2015 are expected to be between £40m and £50m, compared with £87m last year.
As well as Alton Towers being closed, Merlin suspended advertising for its theme parks, and rides at other sites were also closed temporarily.
Merlin said the disruption could continue to affect the profitability of its theme park group in 2016.
Sixteen people on the Smiler rollercoaster were injured on 2 June when the carriage they were in riding in collided with an empty one that had come to a halt on the track.
Leah Washington, 17, had a leg amputated following the accident, while her boyfriend Joe Pugh, 18, suffered severe knee injuries. Vicky Balch, 20, also had a leg amputated, while Daniel Thorpe, 27, suffered a broken leg and a punctured lung.
The victims received their first compensation payments last month. All those on the ride will be compensated.
Chief executive Nick Varney said: "The accident at Alton Towers in June was a devastating event, for which we have accepted responsibility and are deeply sorry.
"We have been humbled by the grace and fortitude of those who were injured, and their families, and will continue to do whatever we can to support them."
Alton Towers could reclaim its position as the UK's favourite theme park, Mr Varley said, but that goal could take between 12 and 18 months to achieve.
"There has been a substantial reduction in the visitor numbers at Alton Towers, and to a lesser extent at Thorpe Park," he said.
"At the end of the day we have had one accident in the history of this company. I think, hopefully, people believe we have been responsible in the way we have acted."
Merlin said it had implemented additional safety protocols to prevent a similar accident in the future.
The Smiler remains closed, but rides at other parks that had been suspended are back in operation.
Analysis: Simon Jack, business presenter
The owner of Alton Towers, Merlin Entertainments, has started assessing the financial cost of the serious accident which resulted in life-changing injuries for five people and closed the park for five days.
The financial hit to the theme park division of Merlin is enormous. Operating profits of nearly £90m could be cut to half that.
On the overall group, which also owns Madame Tussauds and Sea Life, the impact is lower but today's announcement still amounts to a significant profit warning and shares fell 8% in early trading.
Perhaps most telling was the company's admission that the negative overhang from this incident may carry on into 2016. There is a received wisdom in business that people's memories are short. Today's announcement shows that Merlin are not banking on that and realise there is a significant job yet to be done in reassuring rattled thrill seekers.
The profit downgrade was bigger than expected, said Panmure Gordon analyst Anna Barnfather.
Despite the fall in profits from its theme parks division, Merlin said that savings and better-than-expected trading across the wider group meant that annual underlying pre-tax profit would be "broadly in line" with the £249m posted in 2014.
Analysts had expected the company to make profits of £273m this year.
Shares fell as much as 8% in the first few minutes of trade, although they recovered to close down by 4.2% at 405.20p. The shares have risen by about 20% since Merlin floated in November 2013.
Ahead of first-half results due to be issued on Thursday, Merlin said that underlying pre-tax profit was up £9m to £49m, with revenue rising 2.8% on a like-for-like basis, or £31m, to £544m. Revenue from the theme parks division was down 2%.
Visitor numbers across its attractions - which include Legoland parks, Sea Life, and Madame Tussauds - rose 200,000 to 27.7 million.
Merlin said the weak euro had affected visitor numbers at its London attractions, such as The Eye, because the capital was a more expensive compared with the Continent.