Officers said the 24-year-old had been detained in police custody in connection with a serious sexual assault in Queen's Park on 30 March.
The park, at Pollockshaws Road and Balvicar Street, was cordoned off while police investigated the incident.
A report will be submitted to the procurator fiscal, Police Scotland said.

Officers were called to reports of an altercation at the Intu Bromley Shopping Centre at 15:45 GMT.
Video filmed by a member of the public appears to show shoppers fleeing in panic, while a photo shows a police officer holding what appears to be a large knife.
A man in his 20s, who suffered a minor head injury, was arrested.
He was detained on suspicion of affray and possession of an offensive weapon.
Eyewitnesses reported seeing a man holding a machete.
Footage posted on Twitter by Alexander Adeosun, who was shopping with his friends at the time, shows people running through the shopping centre.
"There was panic and people were running and falling over," he said.
"My brother had to jump over the escalator."
Mr Adeosun said he was filming from the floor above and saw police arresting a man.
He said he also saw an officer placing what appeared to be a machete in a bag.
Keith Moon, 35, said he had been shopping with his wife at the time.
"We walked back in and saw the police leading a young guy in handcuffs away. One of the policemen was holding a machete around 2ft long," he said.
Armed officers were called to the scene but their assistance was not needed as it was not a firearms incident, the Met said.
A force spokeswoman said: "At this stage officers believe he sustained the injury as a result of an altercation.
Officers wish to trace "approximately six youths" seen running off from the scene, she added.
Earlier, the Met said it was seeking a man seen fleeing the scene, possibly discarding a weapon
Police recovered two knives from the scene.

The Premiership leaders head to Ibrox for the first time this season having won 5-1 at Celtic Park in September and 1-0 at Hampden Park in the League Cup.
"I think we have progressed since that game, I think we have been even better.
"So if you take that into account, it might be that the gap is bigger," said the Dane ahead of Saturday's clash.
"You always talk about gaps but you also know that one game can change that perception of it.
"So I think the most important thing is to be respectful and say that we are doing our job and Rangers are doing their job.
"If we at the moment are number one that means something, so we will be doing our best to keep that."
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Rangers have taken 24 points from a possible 33 since their League Cup semi-final defeat to move into second place in the Premiership, having won four and drawn one of their last five games.
"They have improved, for sure," Sviatchenko acknowledged. "It is always difficult to come back up into the league but they have performed well and you can see that in the table.
"But I think we are still doing really well and we need to focus on ourselves."
Celtic, chasing a sixth successive league title, are unbeaten in 23 domestic matches this season and have won their last 14 matches in the Premiership.
They are within three matches of equalling the club's 'Lisbon Lions' class of 1966-67 that went 26 domestic matches unbeaten at the start of the season - before losing 3-2 at Dundee United on 31 December.

The now famous photo was taken during a speech in the capital, Bangui, and has been tweeted more than 100,000 times.
Tweeters have been making thousands of imaginary rap lyrics, known as bars, under the hashtag #PopeBars.
The Pope was in the CAR as part of a three-nation tour to Africa which also took him to Kenya and Uganda.
The visit was Pope Francis' first to the continent and he spent six days in the three countries where he was greeted by thousands of the faithful.
In Bangui he also addressed Muslim worshippers in a mosque where he said that "Christians and Muslims are brothers and sisters".
The country has experienced after nearly three years of violence between Christians and Muslims.
After the Pope left the CAR for Rome, Twitter users began to imagine what subjects the pontiff could be rapping about:
Read more about the Pope's visit to Africa:
Police investigating the rape of a 37-year-old woman in a popular Glasgow park have arrested a man.
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A machete has been recovered after a suspected knife fight broke out at a shopping centre on Boxing Day.
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Celtic defender Erik Sviatchenko believes the gap between the champions and Rangers may have grown since their last meeting two months ago.
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A photo of Pope Francis has gone viral on social media after he was captured in a classic rapper pose during a visit to the Central African Republic (CAR).