Amazon's cloud services business has been growing exponentially, but the company still has a long way to go, the division's CEO Andy Jassy told CNBC's Jim Cramer on Thursday.

With $30 billion of revenue run rate and 45 percent year-over-year growth, Amazon Web Services is just getting started, he said.

"It's the early stages of the meat of early enterprise and public sector adoption in the U.S.," Jassy said. "Outside the U.S., they're 12 to 36 months behind, depending on the country and industry. So it's still really early days."

Amazon took a lead in the cloud space because the company has been able to scale its service and cut costs for clients who opt for the platform over building out their own system, he said. It takes a ton of time and capital to build a data center, but AWS offers "speed and agility," he said.

Companies looking to experiment with their own cloud system could wait as much as 12 weeks to receive a server before it can build the software around it, Jassy said. That created a customer base for Amazon.

"In the cloud you can provision thousands of servers in minutes," he said. "And then because we have 165 services that you can use in whatever combination you want, you can get from an idea to implementation in several orders of magnitude faster, so you can innovate much quicker."