Mr Peralta, who also played for the Honduras national team, was found dead in the car park of a shopping centre in La Ceiba on the northern coast of the country.
The midfielder played for Scottish club Rangers for 18 months, helping them win the 2013-14 Scottish League One title but left in January to play for Club Deportivo Olimpia in the Central American country.
He won 26 caps for Honduras and played at both the 2014 World Cup and the 2012 London Olympics.
Honduran soccer player Arnold Peralta shot dead [AMBIENT]
His father Carlos told of his devastation at the news and appeared to blame a group for his death.
He said: "This is terrible. They killed my exemplary son.
"I can't say more because of the pain I feel."
The Honduran Ministry of Security said the car park had its own private security.
Robbery had been ruled out as a motive because the victim had not been stripped of his belongings.
Osman Madrid, director of the Honduran national football federation, said: "This is a tragic death that the national sport mourns."
Mr Peralta's club has also expressed its sympathies online.
Rangers released a statement this morning expressing their sympathy.
"Our thoughts go out to Arnold’s family and friends at this very difficult time," it read.
"The club will pay its respects with a minute’s silence before tomorrow’s game against Morton. The players will also wear black armbands in his honour."