Activists want Kenya National Hospital CEO Lily Koross and Health CS Cleopa Mailu to resign following allegations of rape at the facility.
They said on Tuesday that the chief executive was wrong to "quickly deny" the claims before investigating them.
"Violence against women at KNH is despicable. For Koros to tell women to drop the allegations in a suggestion box is an insult," noted Rita Mutheu, one of the organisers of the protest.
Mildred Owiso, who made the allegations public, said seven women have come out with their cases so far.
"You cannot expect women to just go to police stations to make a report about rape. It is not a walk in the park."
No woman has reported the matter to police.
The cabinet secretary will release a report on the allegations in Mombasa on Tuesday.
Kenyatta National Hospital was put on the spot after a woman claimed she was sexually assaulted when she sought to breastfeed her baby.
Members of the public got angry last Friday when Koros reported that they asked the DCI to investigate as they did not have any record of assault.
In an interview on Citizen TV on Sunday, the CEO defended herself saying she did not deny the claims but issued a statement based on the report they had received at the time.
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