Maxwell, who was rested from yesterday's fifth and final one-dayer against Mahendra singh Dhoni's men, is expected to be available for the second T20 in Melbourne on January 29.
"He has still got a little slight hamstring niggle so ... he will spend a few days in Melbourne at home and join the squad when we get there in a couple of days," acting coach Michael Di Venuto told reporters at airport here.
Di Venuto is doing the interim coaching duties as Darren Lehmann had to be hospitalised after being diagnosed with Deep Vein Thrombosis for the second time in his life.
In Maxwell's absence, Travis Head could make his international debut for the side on Tuesday.
Di Venuto said the upcoming series against India could be considered selection trial for the World T20 in March-April.
"Obviously there is a big carrot at the end of this with the World Cup team being picked, and you can only pick 15 people so we want to give people opportunities to see what they can do," he said.