He was taken to the Royal Sussex County Hospital following the incident just before 06:00 BST on Saturday. He is reported to be in a stable condition.
Sussex Police said the incident in Preston Street appeared to be linked to the collapse of a section of railing surrounding the balcony.
The one-way street had to be closed to allow for investigations.

Jason Van Dyke was heckled as he arrived at court where he denied six counts of first-degree murder.
Video released earlier this year showing the shooting of Laquan McDonald sparked an outcry and the resignation of the chief of police.
A federal investigation into the city's police is under way amid a national debate about the police use of force.
The inquiry will explore whether race plays a part in the police use of force and whether officers are properly held accountable.
McDonald, who was 17 at the time, was armed with a knife when he was stopped by police.
But the dashcam footage showed him moving away from police when Mr Van Dyke opened fire.
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Days of protests followed the release of the video, which President Barack Obama said was "disturbing".
There were calls for Chicago Mayor Rahm Emanuel to resign and Police Superintendent Garry McCarthy quit his job.
On Saturday, Mr Emanuel said the city "deserved answers" after a police officer accidentally shot and killed a 55-year-old woman when responding to a domestic disturbance.
According to the Washington Post, Bettie Jones was also known as a community activist who spoke out on issues such as police brutality.

Steven Hirschorn said his son Ollie was upset when he lost his lion, Liley, at Hughenden Manor in Buckinghamshire.
However, the toy was returned last week along with a photo diary showing Liley driving a buggy and exploring the National Trust property.
Mr Hirschorn said it was "a lovely gesture".
Ollie has had Liley since he was about 11 months old and is so treasured that a back-up had already been bought, in case he ever got lost.
Mr Hirschorn said although the two lions look identical, Ollie could tell the difference and was sad when "good Liley" went missing on Easter Monday.
"He was on the verge of tears when it was pointed out that he wasn't holding Liley," Mr Hirschorn said.
Staff at the former home of Prime Minister Benjamin Disraeli were told of the missing lion, but he remained unfound until two days later.
Charlotte Russell, conservation assistant, said: "He was found in one of the boxes we have on the top floor, it wasn't an obvious place.
"Our office thought it would be a nice idea to take photos of him in different places around the manor - so the boy could see he had had an adventure."
Mr Hirschorn, who lives in west London, said he was impressed by the effort, having thought Liley would be sent back "stuffed in an envelope".
"Straight away Ollie was playing with the stickers they sent and we've told him the story shown in the photos.
"He was very happy to see Liley again."
A 20-year old man is in hospital with serious injuries after he fell from a first floor balcony in Brighton.
[NEXT_CONCEPT]
A white Chicago police officer has denied murder over the death of a black teenager who was shot 16 times in 2014.
[NEXT_CONCEPT]
A three-year-old boy has been reunited with his favourite toy lion, which was photographed having an "adventure" at a stately home after being lost.