The £500,000 vehicle was one of four – including a second coach used by the Ibrox side – gutted by flames at the Bruce’s Coaches depot in the Lanarkshire village of Salsburgh early on Saturday morning.
Although nobody was hurt in the incident, the fire was so intense that it engulfed the corrugated iron garage, reducing it to a molten pile.
It is believed those responsible for starting the blaze gained access by cutting a hole in the metal fence that surrounds the garage.
Rangers manager Ally McCoist said he believed the incident was a “premeditated attack on Rangers’ bus”, but police refused to be drawn on whether or not the vehicle was the target of the attack.
A Police Scotland spokeswoman said that although the fire was being treated as “wilful”, they could not say at this point that the Glasgow team’s bus was a specific target.
She said: “Inquiries are continuing, but we are not going to be drawn into any speculation.
“We are keeping an open mind and would appeal for any witnesses to come forward.”
The coach company owner, John Bruce, said: “It’s devastating. The Rangers buses are among four coaches completely destroyed.
“Luckily no-one was injured and hopefully the police will get to the bottom of it.
“The Rangers bus is not a bus any more – it’s just a heap of scrap.”
The bus, which the club had taken delivery of barely a month ago – was made in the Netherlands and had been decked out in the Rangers tartan, with a private registration plate that read R1 WTP – a reference to the popular terrace chant by team fans of “We are the people”.
It was also fitted with satellite television, kitchen facilities and an area for physiotherapy treatment.
McCoist said that he was “saddened” by the incident. “I think its pathetic that people would go to these extremes,” he said.
“It sounds like a premeditated attack on Rangers’ bus and I’m gutted about it, but thankfully nobody’s been killed.”
Witnesses described a series of explosions as the fire spread through the depot.
One onlooker said: “The flames were sky-high and there were three big explosions.
“The guys in the garage were moving buses away from the fire, which was very brave of them.”
Other witnesses said the explosions made the street outside the garage shake, and that there were fears that the fire would spread to other buildings.
Eight firefighter teams from Coatbridge, Motherwell and Airdrie, along with a paramedic team, attended the depot at 2:40am. The fire was put out shortly after.
A Rangers spokesman said: “The club was shocked to learn of the news and we await the outcome of the police investigation.”
Detective Constable Craig Cheyne added: “It is still very early in our investigation but it is apparent that the fire was set deliberately.
“There has been substantial damage to several coaches and the property and it’s imperative we trace those responsible.
“I am appealing to anyone who may have any information or knowledge regarding this crime to get in touch with us. Even if you think your information may not mean much, let us be the judge of that and please do pass it on.”
As yet, the specific cause of the fire had not yet been identified by investigators.