In a press briefing, he condemned Barnaby Joyce for a "shocking error of judgement".
Mr Joyce will take a leave of absence from Monday amid scrutiny over whether he breached ministerial standards.
Both Mr Joyce and Mr Turnbull deny that any rules, as defined, were broken.
But the prime minister said he would overhaul the "truly deficient" ministerial code of conduct.
"Ministers must behave accordingly. They must not have sexual relations with their staff - that's it," he told reporters.
Mr Turnbull earlier told parliament that Mr Joyce would not fill his post as acting leader next week when the prime minister travels to the US.
The scandal has dominated Australian politics since last Wednesday when Mr Joyce's affair with media adviser Vikki Campion was publicly revealed.
Mr Turnbull said Mr Joyce would be on leave for a week from Monday. Opposition parties called on him to resign.
The high-profile conservative had only returned to parliament in December after briefly losing his job over his New Zealand dual citizenship.
'World of woe'
Mr Turnbull said his deputy had caused "terrible hurt and humiliation" to his estranged wife, Natalie Joyce, their four daughters, and Ms Campion.
"Barnaby made a shocking error of judgement in having an affair with a young woman working in his office," he said.
"In doing so he has set off a world of woe for those women, and appalled all of us. Our hearts go out to them."
On Tuesday, Mr Joyce publicly apologised to all six for what he called a "searing personal experience".
Mr Turnbull said such behaviour was not acceptable "today, in 2018", and ministers must oversee respectful workplaces.
On Thursday, the Senate passed a motion calling on Mr Joyce to resign - although it has no power to force such a move.
Mr Joyce has faced questions over the timing of two unadvertised jobs within his party that were taken up by Ms Campion last year.
Under the code of conduct, Mr Turnbull must approve any ministerial department job given to the partner of a frontbencher. No permission was sought for Ms Campion.
However, both Mr Joyce and Mr Turnbull maintain that Ms Campion was not the deputy prime minister's partner at the time.
Mr Joyce was due to step in as acting prime minister while Mr Turnbull is on his trip to the US, in line with usual convention.
The role will instead be taken up by Mathias Cormann, the government's leader in the Senate.