The customers who had pre-ordered the service, which officially launched yesterday, have been told they may not receive them in time for the start of the football World Cup.
French electronics company Thomson, which holds the contract to supply the set-top boxes to Sky, failed to meet the deadline for delivering the technology.
A spokesman said: 'Sky HD has launched on time with around 2,500 installations on the first day but we are having to change some installation dates because of delays to HD box deliveries. We ordered more than enough boxes to meet demand and we're ready to install them but they're not arriving from our supplier as fast as we agreed.
'We think the fairest approach is to keep installations in the original order. Although this means that any delay to the first installations may have a knock-on effect on others, we believe it is important that those who requested Sky HD first will still be amongst the first to receive it.
'We're very sorry for any disappointment this has caused and we're working hard to resolve the situation. Thousands of customers will have their HD box this week and many more will be installed in time for the start of the World Cup.'
Sky has received more than 40,000 orders for HDTV since it started to take pre-bookings last month.
The backlog is expected to translate into a wait of roughly two and a half weeks, meaning many will now not receive their boxes until after the start of the tournament.