The 29-year-old has not played at the team competition since 2019, showing little interest in making a comeback while grappling with injuries.
But the 2022 Wimbledon finalist was among the nominations put forward for their tie with Sweden after his return to the sport last week in Brisbane following wrist reconstruction.
Kyrgios lost in three tight sets to rising French star Giovanni Mpetshi Perricard and said he would need "a miracle" to be competitive at the Australian Open starting on Sunday.
Hewitt also named world number eight Alex de Minaur, Jordan Thompson and Thanasi Kokkinakis in his four-man outfit.
Australia, last year's Davis Cup semi-finalists, meet Sweden in Stockholm on January 31-February 1.
