The battle between the King Kong and Godzilla of retail has moved into the cloud.

Wal-Mart Stores Inc. is telling some technology companies that if they want its business, they can’t run applications for the retailer on Amazon.com Inc.’s leading cloud-computing service, Amazon Web Services, several tech companies say.

Amazon’s rise as the dominant player in renting on-demand, web-based computing power and storage has put some competitors, such as Netflix Inc., in the unlikely position of relying on a corporate rival as they move to the cloud.

Wal-Mart, loath to give any business to Amazon, said it keeps most of its data on its own servers and uses services from emerging AWS competitors, such as Microsoft Corp.’s Azure.

Wal-Mart uses some tech vendors’ cloud apps that run on AWS, said Wal-Mart spokesman Dan Toporek. He declined to say which apps or how many, but acknowledged instances when Wal-Mart pushed for AWS alternatives.