Customers who pre-ordered Samsung's new top-end smartphone face weeks of delays in receiving their handsets.
The South Korean firm signalled that it had faced issues in manufacturing blue models of the Galaxy S3.
Vodafone added that it had also been advised of "shipping delays" to the 32GB version of the white version of the handset.
Available devices went on sale in the UK and 27 other European and Middle Eastern countries earlier.
"Samsung's Galaxy S3 Pebble Blue version comes with a newly invented blue colour and special hyperglaze material," said a statement from the electronics company.
"In order to meet the highest internal quality standards and to provide the best quality Galaxy S3 to customers, a short supply of [the] Pebble Blue version is expected in some regions in the next two to three weeks."
Vodafone - which has an exclusive deal to distribute white 32GB models in the UK for four weeks - noted that it might take up to that period for customers to receive the delayed models.
It added that "all customers who have pre-ordered the marble white 16GB version... should expect to receive their new phone on the UK launch date".
O2, Everything Everywhere and Three also confirmed their customers would be affected by the "shortage of blue" models.
The Android-based phone is expected to prove highly popular. It features a 4.8 inch (12.2cm) screen, a "natural language user interface" and can track users' eye movements to ensure the screen does not dim while they are looking at it.
The success of its predecessor, the Galaxy S2, helped Samsung overtake Nokia as the world's best-selling phone maker, according to the research firm Strategy Analytics.
Reviews have compared the device favourably with Apple's smaller-screened iPhone.
The Verge declared it a "a technological triumph", although Engadget suggested that HTC's One X had a superior user-interface and design.
Samsung has said it expects the S3 to outsell the S2. It is scheduled for release in 145 countries by July.