The 2004 Olympic silver medallist suffered life-threatening head injuries when a taxi he was in along with a team mate crashed head on into a concrete barrier in the Barra de Tijuca neighbourhood of the city early on Friday.
"There have been no changes to the situation in the last twelve hours which means that he has very, very serious injuries, and his condition is life-threatening," team doctor Bernd Wolfahrt told reporters. "This can be clearly said.
"But out of respect to Stefan Henze and his family we will not make any unnecessary speculations. We are waiting for the relatives to get here."
Another canoe team official, Christian Kaeding, suffered minor injuries and was briefly treated in hospital before being released.
Henze was first treated at a nearby hospital but had to be transferred to another clinic that has a special neurosurgery department.
"Of course the whole team has been affected by this terrible accident and the serious injuries sustained by Stefan Henze," said German team chief Michael Vesper.
"Everyone is shocked and we are all praying and hoping that he can get better soon."
Security and traffic have been a main concern for teams at the Rio Games while several official Olympic buses have been involved in traffic accidents.
(Additional reporting by Reuters Television, editing by Ed Osmond)
