Milne, 30, had some tightness in his hamstring at the end of the home series against India in November 2022 and subsequently missed two Ford Trophy games, New Zealand's domestic 50-over tournament, for Wellington in December.
He played Wellington's first two matches of the Super Smash, the domestic T20 competition, but the workload of six ODIs in 16 days in Pakistan and India was considered too much of a risk.
"Blair's skills at bowling through the middle and his ability to hit the pitch hard make him a similar prospect to what Adam offered us. The fact he's already in Pakistan experiencing the conditions is an added bonus."
New Zealand drew the Boxing Day Test against Pakistan and begin the second and final Test of the series on January 2 in Karachi. The ODI players will leave New Zealand for Pakistan on January 4 for three matches on January 9, 11 and 13 - all in Karachi - before travelling to India for three ODIs on January 18, 21 and 24.
They will also play three T20Is in India on January 27, 29 and February 1; the squad for the T20I series is yet to be named.
New Zealand squad for ODI series in Pakistan and India
Kane Williamson (capt - only for Pakistan ODIs), Tom Latham (capt - India ODIs), Finn Allen, Michael Bracewell, Mark Chapman (India ODIs only), Devon Conway, Jacob Duffy (India ODIs only), Lockie Ferguson, Matt Henry, Daryl Mitchell, Henry Nicholls, Glenn Phillips, Mitchell Santner, Henry Shipley, Ish Sodhi, Tim Southee (Pakistan ODIs only), Blair Tickner.