CA's National Aboriginal and Torres Strait Islander Cricket Advisory Committee recommended the move, with three Big Bash League games to be played on January 26.
The prime minister hit out at the sport's governing body over the decision, which CA argues aims to normalise conversations over the date's history.
"A bit more focus on cricket and a little less focus on politics would be my message to Cricket Australia," Mr Morrison told Rockhampton radio 4RO on Thursday.
"I think that's pretty ordinary."
CA will refer to January 26 instead of Australia Day in its material.
Three BBL teams will also wear Indigenous jerseys in matches on or leading up to the day.
A barefoot circle, welcome to country and smoking ceremony will take place before some games.