"He is improving and the medical staff with the coaches will make a day-to-day assessment on whether he will be available for our next game," a spokesman said.
Carter had not had the injury x-rayed and was back doing light drills with the squad.
The Crusaders are set for a training run today which should give a much stronger idea whether the five-eighths will be fit for Saturday's southern derby with the Highlanders.
"The only way we will really know is if we can do a proper assessment," coach Todd Blackadder said. "At the moment he feels the leg isn't overly serious and we will just see how it goes. We have a little bit of time."
Carter's latest injury is in the same part of his right leg where he cracked a small bone during last year's Super Rugby final. He missed the entire Rugby Championship before passing fitness tests to squeak on to the All Blacks end-of-year tour.
He came off the bench against the USA and started the test against Scotland before being subbed while Aaron Cruden and Beauden Barrett shared the "major" starts against England and Wales.
The Crusaders have enough options for their second game if Carter does not recover.
Coach Blackadder could shift Colin Slade from fullback which would also give Israel Dagg the chance to play or he could move Tom Taylor in one place and have Ryan Crotty in midfield.
All sorts of permutations will be buzzing around Blackadder's thoughts after his side's lacklustre beginning to the 2015 tournament. "We are not panicking by any means but we are certainly not satisfied," he said. "If you don't get a change in behaviour then questions have to be asked. There were a few guys who were outstanding but we just didn't perform as a team and that is just unacceptable."