Former French Open champion Ivanovic joined double grand slam winner Sveltana Kuznetsova (27th), Swiss teen Belinda Bencic (32nd) and Sabine Lisicki (28th) as seeded casualties in early first round action.
Ivanovic, a former Australian Open finalist, had roared through the first set in 21 minutes on Rod Laver Arena and looked set to follow third seed Simona Halep into the second round after the Romanian's 6-3 6-2 win over Italy's Karen Knapp in the first game on the showcourt.
However, Hradecka, who played only three WTA level events in 2014, raced through the next two sets in just over an hour to send the Serb packing and set up a second-round encounter with Slovenia's Polona Hercog or China's Wang Qiang.
"I played okay in the beginning. Just I felt second and third set I really dropped my level," said Ivanovic, whose only other first round exit at Melbourne Park was to Ekaterina Makarova in 2011.
"It was really tough for me to find rhythm a little bit.
"It's really disappointing. It's probably the worst thing (that) could happen.
"But still, the year is young and I really have to now sit and work on few things and just maybe try to have a different approach to this kind of event and try to see what was lacking."
Czech Hradecka, who plays with an unorthodox double handed grip from both sides of the court, is ranked 142nd in the world and has had most of her success as a doubles player with compatriot Andrea Hlavackova.
Ivanovic's exit was the biggest upset in the early stages of the first round, though three other seeded women were also knocked out.
Bencic was hammered 6-2 6-1 by Julia Goerges in just over an hour, while Kuznetsova, the 2004 U.S. Open and 2009 French Open champion, lost 6-4 6-2 to France's Caroline Garcia, and German Lisicki was beaten 4-6 6-4 6-2 by Kristina Mladenovic, also of France.
(Editing by Peter Rutherford)
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