The 22-year-old Dragons second row, who scored his first try for Wales on winning his eighth cap against Scotland last month, will be replaced by 1999 RWC veteran Chris Wyatt.
'Michael injured his back prior to going on our warm weather training camp to Lanzarote and, after seeking specialist advice, we have decided not to risk him by taking him to Australia,' said Wales coach Steve Hansen.
'The injury means he will be out for a further six weeks or so. At 22, he is still a young man and he has a lot of rugby left to play so we have taken the common sense option and decided his long term future is more important than his short term future career.
'Michael understands the situation and we are lucky to have an able replacement in Chris Wyatt to bring into the squad.
'Chris was unlucky to miss out on the final 30-man draft and we are pleased to welcome him back on board.'
Wales - drawn in World Cup Pool D alongside New Zealand, Italy, Canada and Tonga - will leave for Australia next Sunday.