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.
Valentina Ponomaryova
In December 1961, the selection of female cosmonauts was authorized by the Soviet Government, with the specific intention of ensuring the first woman in space was a Soviet citizen. In February 1962 Ponomaryova was selected in a group of five female cosmonauts to be trained for a Vostok flight. The group spent several months in intensive training, concluding with examinations in November 1962, after which the four remaining candidates were commissioned Junior Lieutenants in the Soviet Air Force. Ponomaryova established herself as one of the leading candidates with Valentina Tereshkova and Irina Solovyova, and a joint mission profile was developed that would see two women launched into space, on solo Vostok flights on consecutive days. The honour of being the first woman in space was to be given to Valentina Tereshkova who would launch first on Vostok 5 while Ponomaryova would follow her into orbit on Vostok 6. However, Ponomaryova did not respond with standard Soviet cliches in interviews and her feminism made the Soviet leadership uneasy, and this led to the flight profile being altered in March 1963. Vostok 5 would now carry a male, cosmonaut Valery Bykovsky, flying the joint mission with Tereshkova aboard Vostok 6 in June 1963. Tereshkova's backup was Irina Solovyova, with Ponomaryova in a supporting 'second back-up' role.