Pucovski has played just eight first-class matches but scored 243 for Victoria earlier this season before he opted to take a break from the game to receive treatment for a mental health-related illness.
"Will Pucovski has been released from the men's test squad and will return home to Melbourne to continue managing his wellbeing," Cricket Australia Doctor Richard Saw said in a statement from the board.
"He reported some challenges over the past few days, and the decision has been made that the best thing for Will's welfare is for him to return home to Melbourne.
"Will has been proactive in this process and while he has made significant progress, he feels this is the best course of action to get ready to play cricket for Victoria."
Pucovski consulted his family and Cricket Victoria before arriving at the decision, the board said.
"Will's decision to speak up and continue to ask for assistance in managing his ongoing mental health is extremely positive," Saw added.
"Cricket Australia and Cricket Victoria will continue to support Will, and we kindly ask that Will's privacy is respected so he can continue working towards a return to Premier Cricket and the next round of First Class cricket."
Pucovski did not make the team for Australia's first-test victory in Brisbane and was also overlooked for the ongoing second and final test against Sri Lanka at the Manuka Oval.
(Reporting by Sudipto Ganguly; editing by Toby Davis)
