Halep, who beat Errani 6-4, 6-4 to advance to the semi-finals, received the death threat via Twitter from a Danish fan on Thursday.
As a result of this, the Porsche Tennis Grand Prix organisers have stepped up security around Halep.
However, when asked about the death threat, Halep refused to speak about it.
"I can't comment on it," she told reporters. "I am here to play tennis. Other people will take care of it."
It is also understood that Halep's stalker sent her numerous messages through social media.
Despite this, the 23-year-old has vowed to stay focussed, especially since she will be facing Caroline Wozniacki in the semi-finals after the Dane beat Spain's Carla Suarez Navarro 6-0, 6-3.
"It was a tough game, she defended very well and it was hard to finish points off against her," Halep said about her match against Errani. "I'm looking forward to the semi-finals now."