Astronaut
The first civilian in space was Valentina Tereshkova aboard Vostok 6 (she also became the first woman in space on that mission).
Tereshkova was only honorarily inducted into the USSR's Air Force, which did not accept female pilots at that time. A month later, Joseph Albert Walker became the first American civilian in space when his X-15 Flight 90 crossed the line, qualifying him by the international definition of spaceflight. Walker had joined the US Army Air Force but was not a member during his flight. 
The first people in space who had never been a member of any country's armed forces were both Konstantin Feoktistov and Boris Yegorov aboard Voskhod 1.
Chiaki Mukai
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.