Scots Olympian Sir Chris Hoy was due to front the BBC Two programme Racing Legends, which would have paid homage to McRae, who died in a helicopter crash near his Lanarkshire home in September 2007.
The programme, which was due to have been aired on December 28, was advertised widely beforehand but was pulled from the schedules shortly before the broadcast date.
The BBC said there was ongoing "editing" issues with the programme and it would be shown later this year.
It is part of a series of three programmes about famous racing drivers.
The show also features the rally champion's father Jimmy McRae speaking about the helicopter crash that killed his son.
The 39-year-old rally ace was later blamed by an inquiry into the crash near his home in Lanark, which killed his son, Johnny, five, his friend Ben Porcelli, six, and Graeme Duncan, 37.
The fatal accident inquiry found the crash happened because McRae carried out unnecessary low-level manoeuvres.
In a tweet, Sir Chris, said: "Not sure when BBC racing legends prog about Colin McRae is on, for those of you asking. Will keep you posted."
However, there were claims on one internet forum that the BBC was sensitive about showing the documentary following the controversy over the decision to show a tribute to the late Sir Jimmy Savile, before it emerged he was a paedophile.
One member of a discussion thread about the series wrote that the tragic accident and the subsequent investigations meant it would not have been "appropriate to have given this the go ahead at all".
In the programme, Sir Chris tracks McRae's successes, from Scottish trials champ, through his world rally career, to driving the route of the Dakar rally.
He also gets behind the wheel of McRae's Subaru Impreza over a stage of the RAC Rally, which the Scot won with co-driver Nicky Grist in 1995 to seal his world title.
The other two programmes in the Racing Legends series were shown as planned.
They were a profile of Sir Stirling Moss by Star Trek actor Patrick Stewart, and television chef James Martin telling the story of Sir Jackie Stewart.
A BBC spokesman said: "Racing Legends is a series of three programmes, one of which was always going to transmit in 2013. Editing is still ongoing on one of the billed episodes so there has been a change to the schedule."
A spokesman later added that it is "currently not aware of any legal reasons why the programme should not be transmitted".
He added that no new date for broadcast had been set.
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