Abdullah al-Muhailbi, the information minister, was appointed as acting health minister, the sources said.
Two conservative Sunni Muslim MPs nonetheless went ahead on Saturday with a request to question Mubarak over the fire as well as alleged financial abuses in her ministry and deterioration of health services.
In her letter of resignation submitted on Friday night to Sheikh Nasser Mohammad al-Ahmad al-Sabah, the prime minister, Mubarak accepted "political and moral" responsibility for the incident, which is currently being investigated, the leading daily Al-Qabas reported.
But she also said that she had been assailed by some MPs from the moment she took over the troubled health ministry "for reasons which are no secret to you".
Mubarak, a member of Kuwait's Shia minority, was apparently referring to the opposition of conservative Sunni MPs to her appointment to high office due to her combined Shia and liberal credentials.
Mubarak made history when she became the first female minister in Kuwait in June 2005, taking the planning and administrative development portfolio, one month after parliament passed a bill granting women political rights.
The US-educated women's rights activist, who wears the Muslim hijab, or head cover, has since served as communications minister and was put in charge of the health ministry in the cabinet formed last March.
Mubarak, in her late 50s, also became the first woman MP when she joined the government, since cabinet ministers automatically become members of parliament in Kuwait.