The Prime Minister's Office has suspended an administrative staffer over an "inappropriate" three-month-old Facebook post about Donald Trump, amid a media storm prompted by a Sydney shock jock.

2GB radio reported the executive assistant to Malcolm Turnbull's chief-of-staff Drew Clarke had been suspended Friday afternoon after announcer Ben Fordham inquired about her online activities.

The junior staffer was accused of posting to Facebook a photo of a T-shirt emblazoned with the words "Tuck Frump", a play on the phrase "F--- Trump" and which also promotes an anti-Trump website.

According to 2GB the original post was made in November, but the staffer had the image permanently fixed on her page as recently as January.