The 26-year-old was found dead in the car park of a shopping centre in the town of La Ceiba, where he lived, according to a statement from the Honduran government’s Ministry of Security.
Peralta - capped 26 times by his country - signed for Rangers in June 2013, making 29 appearances over an 18-month spell with the Ibrox outfit.
The Ladbrokes Championship club confirmed a minute’s silence will be held before Saturday’s league meeting with Morton, while Mark Warburton’s side will don black armbands as a mark of respect.
The player had only recently celebrated the birth of a daughter with his partner.
Kris Boyd spent six months playing alongside the midfielder, who returned to Honduras to sign for Club Deportivo Olimpia after his Gers exit.
“It’s just tragic,” Boyd said. “I don’t really know the ins and outs of it so all I can do is pass on my condolences to his family.
“He was always somebody who would come into training with a smile on his face. He worked hard and did everything to the best of his ability.
“You sometimes hear about illnesses taking people away from their families, but to lose somebody because they’ve been shot will be harder to take.
“I only knew Arnie for a few months but I knew exactly how he was as a person. The biggest tragedy for me is that there is a partner there now who will have to bring up a child by herself.”
Rangers also released a statement, which said: “Rangers Football Club is deeply shocked and saddened to hear the tragic news about former player Arnold Peralta.
“The 26-year-old midfielder, who had an 18-month spell at Ibrox and helped the club win the League One title in 2014, was killed in a shooting incident in Honduras (on Thursday night).
“Our thoughts go out to Arnold’s family and friends at this very difficult time.”
Current Gers striker Nicky Clark posted a picture of himself hugging Peralta on Twitter as well as the following message: “Horrible news this morning, rip Arnie.”
One-time Light Blues defender Chris Heggarty, who now plays for Linfield, added: “The world is mad. RIP Arnie.”
Andy Little, another former Rangers forward, said: “RIP Arnie. Shocking news to wake up to and puts many other things in life into perspective. Thoughts are with his family. #RangersFamily.”
Stephen Harvey, a member of the Ibrox club’s backroom staff, said: “Shocked by the news coming through about ‘Arnie’ Peralta. RIP. Thoughts are with his family.”
The Ministry of Security’s statement, reproduced on the website of Honduran newspaper La Prensa, read: “We regret the violent death of the outstanding sportsman Arnold Peralta, a young player of the national team of Honduras.
“The unfortunate incident occurred in the city of La Ceiba, in the parking lot of a shopping centre which has its own private security.”
Robbery was ruled out as a motive for the killing as the statement noted: “At no time was he stripped of his belongings.”
Peralta played at both the 2014 World Cup and the 2012 London Olympics.
His father Carlos told a news conference he was devastated.
He said: ‘’This is terrible. They killed my exemplary son. I can’t say more because of the pain I feel.’’
Peralta joined Rangers from his formative club CD Vida and helped the Glasgow giants win the 2013-14 Scottish League One title but left the club halfway through last season to join Olympia.
Olimpia wrote on their Twitter feed: “We deeply regret the death of @Arnold12_favian (Peralta) and the continuing violent deaths in our country.”
Two posts on the official feed of the Honduran Football Federation (Fenafuth) read: “@FenafuthOrg deeply regrets the tragic death of national team player Arnold Peralta, which has left national football in mourning.
“Our sincere expressions of sympathy and solidarity to the family and friends of Arnold Fabian Peralta.”
Honduras team-mate Andy Najar wrote: “How sad to see news like this. Rest in peace brother. Strength to the Peralta family.”
Striker Carlo Costly added: “Shocked by the news about my friend and colleague Arnold Peralta, miss you friend !!”