Cricket Australia on Thursday confirmed McGrath, 34, had not arrived in Melbourne for the first of the Chappell-Hadlee series matches and would instead rest for an extra few days with his family before rejoining the squad in Sydney for the second game next Tuesday.
McGrath, the player of the Test series against the Black Caps, should take part in the second match but his break gives him a decent rest after bowling in hot conditions in the second Test against New Zealand in Adelaide.
McGrath (289 wickets) will have to wait to overtake Shane Warne (291) as his country's leading One-day wicket-taker, but the rotation policy means the under-bowled Lee will play just his third match in over two months.
Lee played a tour match in India in October and since then has only played a domestic cup match for New South Wales.
The 28-year-old, the 12th man for both Tests against the Kiwis, has already declared himself the fittest he has been in years and can use the Chappell-Hadlee series to keep the pressure on selectors ahead of the three Test series against Pakistan.
Lee recorded figures of 5-42 the last time he played a One-dayer against the Black Caps -- a World Cup match at Port Elizabeth in March last year.
Another player keen to return to the One-day arena is batsman Michael Clarke, who has played 34 Limited Overs games, but this time starts a One-day series with outstanding Test form.
"I think the difference is I feel like I've played against New Zealand, I know it's a different form of the game but I feel comfortable that I've seen the New Zealand bowlers," he said on Thursday.
Clarke has ambitions of batting further up the Australian order and underlined that goal with an unbeaten 105 - his maiden ODI century - in May when he opened the innings with Adam Gilchrist, albeit against an under-strength Zimbabwe in a meaningless clash in Harare.
New Zealand had a solid hit-out on Thursday, beating a Victorian invitational side by 34 runs in a 40-over match.
Captain Stephen Fleming made a brisk 67, Nathan Astle retired on 66 and Matthew Sinclair hit 44, while fast bowlers Ian Butler and Kyle Mills snared three wickets each.