Ms Higgins alleges she was raped by a male colleague inside the ministerial office of Senator Reynolds in March 2019, after security guards let the pair into Parliament House.
A statement from Senator Reynolds' office said she had been admitted to a Canberra hospital following advice from her cardiologist relating to a pre-existing medical condition.
Ms Higgins on Wednesday responded to news Senator Reynolds had been admitted to hospital.
"I genuinely hope (Senator Reynolds) is okay and wish her all the best with her recovery," she tweeted.
Ms Higgins' rape allegation has led to a series of reviews being announced into the culture and processing of harassment complaints in Parliament.
She said she hoped from this "whole horrible situation" there would be "fundamental reform" to processes available to "vulnerable staff" and improvements to the workplace culture in Parliament House.
Senator Reynolds has faced scrutiny over her response to Ms Higgins' allegations, including when she found out about the complaint and who else she told about the incident.
This includes Senator Reynolds' decision not to notify Prime Minister Scott Morrison - who claims he only became aware of the incident last Monday.
Senator Reynolds has apologised to Ms Higgins for her handling of the complaint, saying she had attempted to respect her privacy and agency.
She has also expressed regret for holding a formal employment meeting with Ms Higgins in the same room the alleged rape occurred following the incident.
Health Minister Greg Hunt told reporters Senator Reynolds was “desperate to appear” at the National Press Club event.
“It was only on the strongest medical advice that she took the reluctant decision not to do it,” he said on Wednesday.
“I would very gently counsel anybody who might reflect other than on somebody’s medical condition."
Mr Morrison has called Senator Reynolds to express his concern and sympathy, and to wish her a speedy recovery.
Foreign Minister Marise Payne will act in the role until Senator Reynolds returns from leave.
Ms Higgins is expected to give a formal statement to police on Wednesday to reactive an investigation into her complaint.
She has claimed she felt pressure at the time to not take her complaint further with police over concerns that doing so would impact her career.
Three more women have come forward saying they were also assaulted or harassed by the alleged perpetrator.