Hot enterprise-focused start-up Snowflake Computing said Thursday that it's making its software available on Microsoft's Azure public cloud. Previously Snowflake, which people can use to store and run queries on data, only ran on the Amazon cloud.

The development is a good sign for Microsoft, which lags behind Amazon in the cloud infrastructure business.

Snowflake CEO Bob Muglia rose through the ranks at Microsoft to one of its top positions over more than two decades before leaving in 2011. But the move to add Azure came from strong customer demand, particularly from retailers who compete with Amazon and are nervous about using its cloud services, Muglia told CNBC in an interview.

For example, Nielsen, a company that already used Snowflake on Amazon Web Services, wanted to use Snowflake on Azure for a new product, Muglia said.

"In this case, the customers they were serving were in the retail industry," he said. "A number of those customers, particularly a large one based in Arkansas, have a fairly strong opinion about this."

That's presumably a reference to Walmart, which has preferred not to have software it uses run on Amazon's cloud, as The Wall Street Journal reported last year. Other retailers have been similarly reluctant to depend on Amazon's cloud services, given its e-commerce heft. Kroger, for example, has chosen to .

But some retailers still do use Amazon's cloud, and Muglia said Snowflake itself has some retail customers that are perfectly happy using the software as it consumes AWS resources. It costs the same amount of money to use Snowflake on Azure in the U.S. as it does to use it on AWS, Muglia said.

In another wrinkle, Microsoft Azure does have a cloud-based data warehouse service that could compete with Snowflake.

"It's a fine product. It just doesn't take full advantage of the cloud because of its architecture," said Muglia, who was involved in Microsoft's acquisition of DATAllegro, whose technology, he said, the Azure service is built on.

Snowflake said in January that it had raised $263 million in funding at a pre-money valuation of $1.5 billion.