The decision could provide a clue into the selectors' thinking for the T20 World Cup though the English-born player has so far met with limited success in the international area.
The 25-year-old allrounder had signed to feature in three first-class four-day County Championship fixtures and the entirety of the T20 Vitality Blast group phase but will no longer travel.
He would have gone to England in May and stayed until the end of July.
The T20 World Cup in USA and the Caribbean runs June 1-29.
Hardy played a key role in the Perth Scorchers' Big Bash campaign, including captaining the side, before taking on the West Indies in white-ball fixtures earlier this year.
Later this week, he will represent Western Australia in the Sheffield Shield final.
Surrey said in a statement that "after a busy year, Cricket Australia have now decided to give him a longer period of rest and therefore he will not be available for Surrey."
Surrey's director of cricket, Alec Stewart, received a personal call from Hardie and accepted the decision.
"Whilst we are obviously very disappointed that Aaron will not be joining the team this summer, I respect the decision of Cricket Australia and wish Aaron the very best," the former England captain said.
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