Reinach plays for Montpellier in France’s Top14 and started Sunday’s victory for South Africa, which came amid complaints by France captain Antoine Dupont about the performance of referee Ben O’Keeffe.
"Gang of thieves, easy to win the title by cheating," the social media post said in French along with a death threat.
South African Rugby have reported the incident to authorities, while Stick said Reinach, who starts in the semi-final against England on Saturday, had taken it in his stride.
"I've seen him every day. He's in a good space. He's got his family around him," Stick told reporters on Friday.
"From our side, we will make sure we protect each other as a team, our players, managers, everyone involved.
"We don't have a place for that. You win some, you lose some. That's part of the game."
Stick said they were happy with the security around the tournament.
"I must give credit to the French (organisers), the security around our hotels is another level.
"So I don't think at the moment there is something to worry about because we know for sure we are well protected in our camps."