The 67-year-old was charged in October with concealing a serious indictable offence allegedly committed by another person.
At the time his lawyer told a court Mr Houston would plead not guilty, a position the pastor reinforced in a statement on Sunday saying he welcomes the opportunity to "set the record straight".
"The board and I have had detailed discussion around the requirements for leadership. 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," Mr Houston said.
"The result is that the Hillsong Global Board feel it is in my and the church's best interest for this to happen, so I have agreed to step aside from all ministry responsibilities until the end of the year."
NSW Police investigated the matter for two years after the allegation was raised in media and at the institutional child abuse royal commission.
They will say Mr Houston's father Frank indecently assaulted a male in 1970.
Court documents allege that between 1999 and his father's death in 2004, Brian Houston believed his father had committed the crime.
Mr Houston initially stepped down from the board of Hillsong, the church he founded with wife Bobbie in Sydney's Hills district in 1983.
Now a global empire, the church says 150,000 people in 30 countries attend its services and 50 million people sing its songs each week.
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