Terms of the deal were not disclosed.
Amazon said in a statement it would incorporate Wickr in its Amazon Web Services (AWS) division which offers cloud computing and other services.
AWS will continue to offer Wickr services including end-to-end encrypted communications which meet certain regulatory requirements.
"The need for this type of secure communications is accelerating," said AWS vice president Stephen Schmidt
"With the move to hybrid work environments, due in part to the Covid-19 pandemic, enterprises and government agencies have a growing desire to protect their communications across many remote locations."
Wickr has touted its "military-grade" encryption for business and government users, and was among the apps reportedly used to leak information from the White House during the Trump administration.
Other apps offering encrypted communications include Facebook-owned WhatsApp, Apple's iMessage and foundation-operated Signal.
These apps can allow people to send messages which cannot be intercepted or read by law enforcement authorities.
The news comes following a congressional panel's approval of legislation which could limit the ability of large technology firms to acquire rivals that would limit competition.
