The accident, which resulted in four 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 trading period.
Profits for the theme parks division in 2015 are expected to be between £40m and £50m, compared with £87m last year.
Panmure Gordon analyst Anna Barnfather said the profit downgrade was bigger than expected.
As well as Alton Towers being closed, Merlin also suspended advertising for its theme parks, and rides at other sites were also closed temporarily.
However, 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.
That reassurance was not enough to stop Merlin's shares falling as much as 8% in the first few minutes of trade, although they recovered to be down 3.5% at 408p by mid-morning. The shares are up about 20% since the company floated in November 2013.
Nick Varney, chief executive of Merlin, said Alton Towers could reclaim its position as the UK's favourite theme park, but that goal could take between 12 and 18 months to achieve.
"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," he said.
Merlin said it had implemented additional safety protocols to prevent a similar accident in the future and was committed to support those injured last month.
Leah Washington, 17, had a leg amputated following the accident on 2 June, while her boyfriend Joe Pugh, 18, suffered severe knee injuries. Vicky Balch, 20, and Daniel Thorpe, 27, were also seriously injured.
The victims received their first compensation payments last month. All 16 people on the ride will be compensated.
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.
