The Bluebirds were initially offered 1,000 restricted tickets, where supporters swap a voucher for a match ticket en route to the stadium, but rejected the offer and then turned down a second allocation of 500 unrestricted tickets out of principle.
Leeds, who have rejected a request for the game to be beamed back, were allocated 2,000 seats for the fixture in south Wales earlier in the season and Cardiff believe their fans are not being shown the same amount of respect.
Cardiff chief executive Ken Choo said in a club statement: "It's extremely disappointing to have reached this conclusion, but having listened to collective views and in knowledge of the positive record and reputation Cardiff City fans have built at away fixtures in recent years, we have no option but to return the low number of unrestricted tickets on offer out of respect for our supporters.
"Our preference was for Cardiff City fans to be granted the same respect and freedom of travel as provided to over 2,000 Leeds supporters for the corresponding fixture this season, and we are frustrated that this could not be permitted.
"We consider the event to be routine and manageable and that that the travel and ticket restrictions in place are substantially out of proportion to any perceived risk.
"For the game on Saturday we are frustrated at not being able to support our players in what we consider to be fair numbers and also question the rationale in denying our request to show the fixture via beam-back at Cardiff City Stadium."
Leeds said they were "disappointed" with the outcome but hope to come to an agreement for next season's fixture.
A statement read: "The club is disappointed to announce that there will be no supporters at Elland Road from Cardiff City at this Saturday's Sky Bet Championship fixture.
"Cardiff City Football Club were originally offered 1,000 tickets as part of a voucher-to-ticket exchange including a new escorted coach system for their family season ticket groups.
"This was rejected by Cardiff City who declined the 1,000 tickets offered.
"After further consideration Leeds United offered Cardiff City Football Club 500 tickets with unrestricted travel.
"Late on Wednesday April 8 Cardiff City notified Leeds United that they did not wish to take up the second offer of 500 tickets unescorted, and that no supporters would travel to Leeds for the Championship fixture at Elland Road.
"Leeds United have consulted with West Yorkshire Police and The Football League regarding this matter and Leeds United will continue to work with Cardiff City to try and reach a mutually agreeable solution for next season's fixtures, both at Elland Road and at the Cardiff City Stadium."
Millwall are forced to travel to Elland Road under similar circumstances, with supporters made to collect their matchday tickets at a service station on the M1, and then boss Ian Holloway heavily criticised the system after the Lions' game there in February.
"It's only when we play Leeds, we don't get it anywhere else," Holloway said.
"It's not an issue anywhere else I don't get it. Years ago it was fashionable to do certain things, but we've moved on.
"For me, West Yorkshire police, get off your arse and don't treat our supporters differently to anyone else."
Source : PA