The 21-year-old McDermott, who was the leading wicket-taker in Australia's domestic one-day competition last season, replaces Clint McKay in the squad for the three-match series after the bowler pulled a hamstring during a practice match in Darwin.
"Alister was impressive in all formats last summer and bowled very well for Australia A against Durham last week," said national selector John Inverarity.
"He is a very fit and disciplined young man who bowls with good sense and good control."
His father Craig played 71 tests and 138 ODIs from 1984-1996, and in a year-long stint as head bowling coach, oversaw Australia's 4-0 whitewash of India in the test series earlier this year before stepping down in May.
The younger McDermott, who shares his father's red hair and possesses a similar bowling action, has raised big expectations in Australia since winning a rookie contract with Queensland state when still at high school.
Australia play their first ODI against Pakistan on Aug. 28 at Sharjah.