The lethal left-arm paceman was the star of Australia's 5-0 Ashes clean sweep of the tourists with his express bowling, finishing with 37 wickets at 13.97.
Johnson will miss Sunday's opening one-dayer in Melbourne but will return for the second match at the Gabba on January 17.
"It's obviously been a big summer for him so we will just give him a short break," Lehmann told reporters. It's about making sure he is fresh for the other one-dayers as well.
"Mitch will play in Brisbane definitely. It's one of his home towns. We want them to play in their home state."
It is likely that Test stars Michael Clarke, Brad Haddin and Shane Watson could also be given matches off during the ODI series, the coach added.
The losing Ashes team from the past three series has bounced back to win the subsequent one-day tournament, including England in 2006-07 when they were also crushed 5-0 in the Test matches.