The company had been working to launch a fertility monitoring device and companion smartphone app for the past four years as part of a project codenamed "Encore," said the people, who asked not to be named because they weren't authorized to speak to the press. The team sat within Amazon's Grand Challenge, also known as its Special Projects division, the sources said.

In October, Amazon told people working on the tracker that it was disbanding the team. Those being laid off will remain on Amazon's payroll until Dec. 27, but won't be expected to work during that time, according to documents reviewed by CNBC.