Bach had already said he would miss Wednesday's opening ceremony to remain in Germany for the funeral of his friend Walter Scheel, the former West German foreign minister and deputy chancellor who died last month aged 97.
But officials said he was now unable to reschedule other commitments and will be unable to travel to Brazil after the funeral.
"President Bach was planning to attend the Opening Ceremony and first day of competition, but can no longer attend due to a State funeral in Germany," Craig Spence, the IPC's Director of media and communications, said in a statement.
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"We fully understand that he cannot reschedule other long standing engagements to attend the Games here at a later date. The IOC is the IPC's number one strategic partner and we thank them, and President Bach, for their continued support."
It will be the first time the IOC president has missed the opening ceremony of the Paralympic Games since 1984.

Thomas Bach

Image credit: Eurosport

The IPC did not say what the long-standing engagements were, but it is not unusual for the IOC president to attend only the opening ceremony and first day of competition.
Bach was in Sochi for the Winter Paralympics in 2014 only for the first couple of days.
"The fact that he can't come is unfortunately a fact of life and shows how busy these presidents and officials are," Spence told Reuters in a telephone call. "We don't see it as a snub at all."
Bach appointed Sam Ramsamy, the IOC Delegate Member to sport for athletes with a disability, as the organisation's official representative at the Opening Ceremony at the Maracana stadium on Wednesday evening.
Rio was awarded the right to host the 2016 Olympic Games and Paralympics in 2009.
The Games run from Sept. 7-18.
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