"Our hearts go out to them. It has been a dreadful thing for them to go through in the glare of publicity."
Joyce, 50, has been under immense pressure since his affair with former media advisory Vikki Campion, 33, who is now pregnant with their child, became public last week.
It has led to allegations that he breached ministerial rules, with the crisis dominating the front pages and parliament question time, with calls mounting for him to resign.
Joyce, whose National Party is in a coalition with the prime minister's Liberals, will take leave next week, allowing him to side-step the role of acting leader while Turnbull is on a visit to the United States.
Turnbull departs for Washington next Wednesday for meetings with US President Donald Trump and is scheduled to be overseas for four days.
Foreign Minister Julie Bishop, as deputy Liberal leader, would normally step in if Joyce was unavailable. But she will also be travelling, which means Senate leader Mathias Cormann will take the position.
Turnbull said the break would allow Joyce to "consider his own position".
The prime minister could sack him, but that risks fracturing the ruling coalition and could cause a rift between the Liberal and National parties.
Joyce admitted to the affair after a picture of his pregnant lover was splashed across the front page of the Sydney Daily Telegraph, and has publicly apologised to his shattered wife of 24 years Natalie and their daughters.
Turnbull said times had changed and people expected politicians to set an example.
"I am not here to moralise. But we must recognise that whatever may have been acceptable or to which a blind eye was turned in the past, today, in 2018, it is not acceptable for a minister to have a sexual relationship with somebody who works for them," he said.
"It is a very bad workplace practice. And everybody knows that no good comes of it."
As such, he amended the code of conduct to make unequivocally clear that "ministers, regardless of whether they are married or single, must not engage in sexual relations with staff".
Joyce -- best known internationally for threatening to euthanise Hollywood star Johnny Depp's dogs over a quarantine violation -- denies he breached any rules, which could be grounds for him to be removed from office.
He has defended the two jobs, one for a minister, that Campion was given after she stopped working for him last year.
The code stipulates that "partners" of ministers cannot be given jobs in ministerial offices without the express approval of the prime minister.
Joyce is also under fire over revelations that he accepted a rent-free apartment from a millionaire friend after his marriage collapsed.
Labor accused him of breaching ministerial standards by asking for a place to live, and in effect receiving a gift of not paying rent for six months. Joyce insists it was offered and he did not ask for it.
Joyce was re-elected in his rural constituency in New South Wales late last year after being forced to stand down over a once-obscure rule barring dual citizens from federal office.
He campaigned on a platform of being a pillar of the community who upheld conservative values, including marriage.AFP.