The 32-year-old Serb will return to court at midday on Saturday trailing 6-2 3-6 3-1 and with plenty of work to do if he is to get a crack at Rafael Nadal in the final.
Top seed Djokovic is bidding to become the first man in the professional era to twice hold the four big prizes in tennis simultaneously, having also done so in 2016.
In gusty winds Thiem's powerful groundstrokes helped him dominate the first set and Djokovic was in trouble early in the second when he fended off a break point.
He got the crucial break in the eighth game of the second set, however, when a Thiem forehand kissed the net cord and flew long and Djokovic levelled the match.
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With dark clouds closing in Thiem broke serve with a huge forehand early in the third, shortly before the rain started again.
Play was eventually cancelled for the day about 50 minutes later despite no rain falling -- leading to criticism from former French Open champion and pundit Jim Courier.
"This is going to sting," the American, commentating for ITV, said. "These conditions are very difficult for Novak, these are very advantageous for Dominic Thiem.
"(Rafael) Nadal and (Roger) Federer came ready to accept the conditions and so did Thiem. But Novak came ready to not like them. The happiest person right now would be Novak on his way back home."
Tournament director Guy Forget denied suggestions that Djokovic had left the grounds before play was postponed.
"I do not know who left first, but the two players were told exactly at the same time. They looked at each other and said 'OK'."
The semi-final will resume at 1200 local time (1000GMT) on Saturday, organisers said.
With 11-times champion Nadal safely through, organisers said they still hope for a Sunday finish.
Nadal beat Roger Federer in straight sets in the first semi when strong winds also hampered the players.
(Reporting by Julien Pretot and Martyn Herman; Editing by Ossian Shine and Toby Davis)
