Barrett missed the All Blacks' final 28-14 win over Australia in Perth on Saturday due to a shoulder injury but will be available for selection in the 36-man squad ahead of the November 1 test against Ireland in Chicago, Robertson said.
Winger Caleb Clarke and prop Ethan de Groot will also rejoin the squad after both missed Perth due to injuries but Robertson must find replacements for lock/flanker Tupou Vaa'i, winger Emoni Narawa, scrumhalf Noah Hotham and prop Tyrel Lomax.
Lomax needs surgery on a broken thumb while Vaa'i may also go under the knife for a knee meniscus injury at training.
"He clicked his knee the week before. He got through training but then he stood up and it locked on him," Robertson told New Zealand media.
"He’ll see the surgeon now so it’s tough for him, he’s been in good form."
Following Ireland, the All Blacks play Scotland at Murrayfield, England at Twickenham and Wales in Cardiff in November tests.
New Zealand's win in Perth had them finish second in the Rugby Championship behind South Africa, who claimed back-to-back titles after beating Argentina at Twickenham.
An Argentina win would have gifted the All Blacks what could be the last Rugby Championship title to be played for years - if the Southern Hemisphere tournament ever resumes.
New Zealand and the Springboks opted out of playing another edition next year, organising instead for the All Blacks to do a full tour of South Africa in 2026.
Robertson and his staff came under fire after the All Blacks lost in Argentina for the first time against the Pumas, then suffered a record 43-10 defeat by South Africa in Wellington last month.
However, back-to-back wins over Australia relieved the pressure, and left Robertson talking up his squad's improvement.
"There’s some things we’re making really good progress in like the aerial battles," he said.
"Some set-piece stuff can make a big difference week to week. We feel like we’ve done that pretty quickly.
"It would've been nice to have had another crack at the Springboks this year but we'll get plenty at them next year."