Boufal, who was part of Morocco’s team that reached the World Cup semi-finals in Qatar 14 months ago, was injured in training over the weekend.
“I think his Cup of Nations is over, and so we’ve lost an important player," Regragui told a press conference.
"It happened in training, as it could happen in a match. It's a muscle injury that will prevent him from finishing the tournament, apart from a miracle. We'll see, but as it stands right now, it’s very complicated for Sofiane.”
Ziyech scored the first-half winner in Morocco’s 1-0 win in their last Group F game against Zambia in San Pedro on Wednesday but went off at halftime with a sore ankle.
“The decision for Ziyech will be made at the last minute or last second,” Regragui added on the eve of the match.
“He was kicked in the ankle against Zambia. We will do our best to get him on the pitch and if we have to take a risk, we will take it because we want our best players on the pitch.
"I think it would be disrespectful to South Africa and to football to say that we can do without Hakim Ziyech and think we could still get to the quarter-final,” he said.
Morocco were among the pre-tournament favourites and topped their section. South Africa were runners-up in Group E.
They are the only team to have beaten Morocco in their 12 matches since the World Cup. The two countries shared the same qualifying group for the tournament in the Ivory Coast.
