Rangers blamed the cost of high level policing "dictated by Police Scotland" for the decision.
The move comes in the wake of the "shame game" at Firhill, home of Partick Thistle, last April.
Rangers revealed the Under-20s clash against rivals Celtic next Tuesday will be played behind closed doors.
A decision has also been made to host Celtic v Rangers, at Celtic Park on May 6, under the same circumstances.
It was made after talks between both sides of the Old Firm, Police Scotland representatives, and SPFL officials.
A statement on Rangers' website read: "After consultation with Celtic, Police Scotland and the SPFL the decision has been taken to play the forthcoming home and away SPFL Under-20s League matches against Celtic behind closed doors.
"This is primarily due to the high level of police presence dictated by Police Scotland and the resulting costs of such required policing."
Trouble flared at the final of the under-17s Glasgow Cup, which was the first meeting of the Old Firm since Rangers were relegated to the Third Division.
Kick-off was delayed after flares and smoke bombs were set off and seats ripped up in the stands.
Fans were also reported to have invaded the pitch at the match, which was attended by around 6000 supporters. Rangers won the game 3-2.
The disgraceful scenes led to a series of arrests as police reviewed CCTV in a bid to find the thugs behind the trouble.
One Rangers fan was banned from attending football matches for two years for making a Nazi salute at the match.
Kevin Brannigan, 28, from Glasgow, was filmed by police making the Nazi salute towards Celtic fans.
He pleaded guilty to the offence and was given a two-year football banning order at Glasgow Sheriff Court.
Meanwhile, Partick Thistle moved to ban Celtic supporters from their historic main stand after the trouble-torn match.
It came after both police and officials raised fears that flare-carrying fans could burn the wooden structure to the ground.
No-one from Police Scotland was available for comment last night.