The bats, together valued at 40,000 Australian dollars (39,050 US), were taken from a shop in the northern city of Darwin. Thieves smashed in a front window, police said.
Shop manager Graeme Flesfadar told AFP the bats were part of a rare set of memorabilia and were irreplaceable. Thieves had clearly targeted them specially.
"They knew exactly what they were after. They didn't touch the till," he said, saying the set was being kept for his children.
"It was being put aside for my kids. I just want it back. Money is not going to replace it."
Darwin police official Gavin Kennedy said it would be hard to sell the items within Australia without being caught and expressed optimism the thieves would be tracked down.
Bradman, who died in 2001 at the age of 92, is regarded as the greatest batsman of all time. He achieved a Test average of 99.94 in his 20 years of playing international cricket for Australia between 1928 and 1948.