“Last year, I also received unexpected news of charges against me that allege the concealing of information that may have been material to prosecute Frank Houston,” Mr Houston said in a statement.
“These allegations came as a shock to me, and it is my intention to vigorously defend them.”
Mr Houston said he and the board of Hillsong have had “detailed discussion around the requirements for leadership” after he stepped aside from all Hillsong boards last year.
“We have talked about the effects of the situation with my father, which go back many years up to the current legal case, and the impact this has had on me emotionally,” he said.
Police allege Brian Houston knew from September 1999 that his father Frank Houston, who died in 2004, indecently assaulted a male in the 1970s.
In a court hearing last November, police argued Mr Houston knew information that could help secure the prosecution of his father and failed to bring it to the attention of police.
Mr Houston had promised when charged in August to “set the record straight”.
“These charges have come as a shock to me given how transparent I’ve always been about this matter,” he said at the time.
At the time, Hillsong Church said it was “disappointed” by the charges.
“We are disappointed that Pastor Brian has been charged, and ask that he be afforded the presumption of innocence and due process as is his right,” the church said in a statement. “He has advised us that he will defend this and looks forward to clearing his name.”
Mr Houston founded Hillsong in Sydney with his wife Bobbie in 1983.
Since then, the church has transformed into a global empire, with 150,000 people in 30 countries attending its services and 50 million people singing its songs each week.
Mr Houston said Pastors Phil and Lucinda Dooley will act as Interim Global Senior Pastors in his absence.
Anyone seeking information or support relating to sexual abuse can contact Bravehearts on 1800 272 831 or Blue Knot on 1300 657 380.