The Hurricanes skipper is making a good recovery after being knocked unconscious during the first half of his side's 48-14 loss to the Bulls in Pretoria on Sunday.
Smith had precautionary scans on his neck following the heavy blow to his head as he made contact with Bulls centre JJ Engelbrecht but they came back clear.
He went underwent a psychometric test after the game, which he failed, but will continue to be monitored during the week.
Hurricanes coach Mark Hammett said the 31-year-old would stay with the side in South Africa as they build towards their game with the Cheetahs in Bloemfontein on Saturday morning (NZT) but wouldn't be available for selection.
There has been speculation surrounding Smith's future in the game given he failed a sideline concussion test during the Hurricanes' first game of the year against the Blues and has also copped head knocks in the past.
But New Zealand Rugby's medical director Dr Ian Murphy told Radio New Zealand's Nine to Noon programme yesterday that if Smith was managed correctly there was no reason why he couldn't continue to play on.
"There is not a compelling reason in terms of research worldwide as it stands that Conrad should stop playing because he has had X number of concussions or there is an evidential cumulative effect that he is a great risk of becoming part of," Murphy told the programme.
"That is not to say that clearly concussion is not a pleasant thing to be having happen to you and if you are having a number of concussions there are other considerations that might come in to your mind around whether you wish to continue to play or not.
"Now there has been no discussion like that with Conrad and obviously any discussion in that regard would have Conrad at the centre of it. But it's not a decision based purely on some guideline that exists out there that clearly shows a contra indication to Conrad continuing to play but there are a host of other factors that come in to these decisions."
There has been research from the United States which suggests that repeated concussions can cause long-term damage to athletes who participate in contact sports.
Dr Jon Simcock, medical adviser for the Neurological Foundation of New Zealand, said on the same radio programme the research surrounding former NFL players who suffered health problems due to repeated concussions showed they weren't managed properly.
"The gridiron players that have gone on to have those major problems concealed the fact that they had multiple concussions and this sets them apart from the rugby players," Simcock told Radio New Zealand.
"So American football players have had repeated and significant concussions which they have withheld from the coaches because they want to keep playing and you can't really extrapolate that to the New Zealand situation of rugby playing with relatively good observations on concussion in our rugby players."
Hammett said there would be no pressure on Smith to make a speedy recovery and he would be monitored carefully.
"Like all injuries, particularly these types of injuries, we've got to be really careful and monitor them. But there's no doubt we've got the best people looking after that and Conrad's a very, very smart man as well, there's no way he'd put himself at undue risk."
The Hurricanes team to meet the Cheetahs will be named on Thursday.
