Swiss authorities searched the sport's head offices in Switzerland and the Egyptian's home on Thursday, the Hamburg prosecutor's office said.
It said it was investigating Mostafa on suspicion of "bribery and corruption ... due to irregularities in the marketing of sports rights," spokesman Wilhelm Moellers told reporters.
He said they were looking into payments allegedly made to Mostafa by a sports marketing firm in 2007 after having been awarded the marketing of TV rights for 2006-09.
The IHF, contacted by Reuters, refused to comment, saying the federation would issue a statement later on Friday.
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