Mukai graduated from Keio Girls Senior High School in Tokyo, in 1971. She received her doctorate in medicine, Keio University School of Medicine, 1977; a doctorate in physiology, Keio University School of Medicine, 1988; board certified as a cardiovascular surgeon, Japan Surgical Society, 1989.

In 1985, Mukai was selected as one of three Japanese Payload Specialist candidates for the First Material Processing Test (Spacelab-J) which flew aboard STS-47. She also served as a back-up payload specialist for the Neurolab (STS-90) mission. Mukai has logged over 566 hours in space. She flew aboard STS-65 in 1994 and STS-95 in 1998. She is the first Japanese woman to fly in space, and the first Japanese citizen to fly twice.

As a NASDA astronaut, she was a visiting scientist at the Division of Cardiovascular Physiology, Space Biomedical Research Institute, NASA Johnson Space Center, from 1987 to 1988. Mukai has remained a Research Instructor of the Department of Surgery, Baylor College of Medicine, Houston, Texas, since 1992. From 1992 to 1998 she was a visiting associate professor of the Department of Surgery, Keio University School of Medicine, Tokyo, and in 1999 was promoted to a visiting professor of the university.

On October 1, 2003, NASDA merged with ISAS (Institute of Space and Astronautical Science) and NAL (National Aerospace Laboratory of Japan) and was renamed Japan Aerospace Exploration Agency (JAXA).

In 2007, Fuji Television released a special episode of its program A Woman’s Biography. The episode is based on the biography of Mukai Chiaki and stars Miho Kanno.

Mukai was assigned the deputy mission scientist for STS-107. In that capacity she coordinated science operations for this science mission. In 2009 Mukai was a visiting lecturer at the International Space University.

From April 2011 until 2015, Mukai was a senior Advisor to the JAXA Executive Director. In addition, she became the director of the JAXA Center for Applied Space Medicine and Human Research (J-CASMHR) in July 2012.

In March 2015, Mukai became vice president of the Tokyo University of Science, and is a technical counselor for JAXA. Since June 2015, she has been Director of Fujitsu Limited and is a corporate executive fellow of Kao Corporation since January 2016.