From there, Smith was taken to hospital where he was subject to tests on his head and neck, but they all eventually came back clear.
Smith said a decision was made by him and team management shortly after the Bulls game that he would not play the following two matches.
Given the Hurricanes have the bye next week, Smith's return is likely to be on May 31, when the Wellington-based franchise meet the Brumbies in Canberra.
Smith served as water boy during the Hurricanes' 39-34 win over the Cheetahs in Bloemfontein on Saturday morning (NZT) and said he had suffered no side-effects of concussion.
"They're just so different. I think people that experience them know and after that knock, within probably half an hour I actually could remember everything about the day right up until the tackle," Smith said.
"Other people experience mass memory loss, guys get headaches, guys can't concentrate, can't sleep; I had none of that in the days that followed. I felt really good. It surprised me a bit."
The 31-year-old has received plenty of support from back home and said he had phoned family and friends while in South Africa to ease their concerns about his health.
Smith said the most worrying aspect was watching a replay of the collision.
"I watched it the following day. More to see how it happened. But that strangely enough was the frightening thing, seeing it; because I didn't feel that bad. Half an hour after I felt like I'd come to."
Smith said he never contemplated retirement and expected to move back to contact work next week with the Hurricanes.
Given the French meet New Zealand in a three-test series next month, All Black coach Steve Hansen will hope Smith can return to the field against the Brumbies and prove his fitness in time to claim the All Blacks' No13 jersey.