Hansen confirmed lock Whitelock suffered damage to his rib cartilage midway through the first half in Napier while flanker Messam injured his quad in scoring the All Blacks' second try, which made it 13-6 at half-time.
New Zealand face a quick turnaround in matches with South Africa visiting Wellington this coming Saturday and Hansen has confirmed Whitelock and Messam will be touch and go to be fit for their final Rugby Championship clash against the Springboks on October 4.
"He's [Whitelock] sore. He's got a rib cartilage rather than a rib fracture," said Hansen. "We will see over the next few days how that comes right.
"Worst case he's out for four weeks, best is three. He's [Messam] not OK. He has done a quad and again he's three to four weeks off as well."