The 28-year-old announced on Monday morning that he wouldn't be competing in either tournament, and pinpointed the clay season as a possible return date.
It's now been nine months since the former US Open champion took to the court, after he suffered a wrist injury in Majorca last June.
The Austrian star originally hoped to be back fit for January's Australian Open, but now in March it seems Thiem is still struggling with his recovery.
Due to his inactivity, the former world No.3 has seen his rank drop to as low as No.50, but that hasn't rushed him into returning, with Thiem preferring to make his comeback in the clay season.
He took to Instagram on Monday morning to inform his followers of the news:"Hello everybody, I wanted to give you a quick update.
"I had really good practice weeks. The wrist is perfectly fine, the hand is getting better and better, but still I decided to pull out of Indian Wells and Miami to start on the clay court. It's still the surface where I feel the most comfortable so I think it's the perfect time to start there."
The BNP Paribas Open in Indian Wells begins on Thursday, and Thiem joins Roger Federer, Novak Djokovic and Andy Murray in being absent from the draw.
Current world No.1 Daniil Medvedev will be looking to capitalise on the weakened pool of players, but he'll have to fight off a revitalised Rafael Nadal looking to win a fourth consecutive title to start the season.
Britain's Cameron Norrie will also be looking to piece together a strong run as he looks to defend the title he remarkably won in the delayed 2021 event last autumn.