Some customers who had pre-ordered the title received it days before the launch day.
Rockstar North, the title’s Scottish creator, is reportedly investigating but has yet to comment publicly.
Amazon said only “a small number” of customers had been affected.
“We have established processes in place to deliver new titles to customers on their release date and are looking into the circumstances that led to a small number of customers receiving this game earlier than intended on this occasion”, an Amazon spokesman told the BBC.
Will Guyatt, spokesman for video and entertainment site IGN.com, told the BBC: “I got an early copy on Saturday, which I paid for myself, and was delighted on a personal level. But it’s obviously going to cause problems for Rockstar.
“There are about 2,000 shops stocking the game ready for launch on Tuesday, so the number of people posting spoilers online is a bit sad”, he said.
Mr Guyatt said he had ordered his copy of the 18-rated violent crime game in March, but others in his office who had ordered it at a later date had not yet received their copies.
“This kind of thing has always happened in the games industry, but with the rise of social media a lot more people know about it now”, Mr Guyatt said.
“I can’t see what Rockstar can do about it.”
Some retailers, such as Cex, have been selling pre-release copies of the game for up to £75, the BBC has learned, nearly double what other stores are planning to charge.
One Cex employee confirmed that there were 13 copies of the game available in a north London outlet, and 25 available in an east London store.
This is not the first pre-launch leak the games maker has had to cope with.
In August, Sony apologised to Rockstar after audio from the forthcoming title was leaked online.
Customers who had pre-ordered the game were allowed to download a “locked” version, but some were able to extract audio that revealed some of the plot lines.
The latest version of the best-selling video game succeeds version 4, first released in 2008, with all the titles in the series selling more than 135 million copies.
A report in the Scotsman newspaper suggests the development costs for GTA5 could be in the region of £170m ($265m; 203m euros), making it one of the most expensive video games ever made.
The report anticipates that GTA5 could rake in £1bn in sales over its lifetime.
Such speculation has helped push the share price of Rockstar’s US owner, Take-Two Interactive Software, up by 65% over the past year.