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 Tereshkova
After watching the successful launch of Vostok 5 on 14 June, Tereshkova began final preparations for her own flight. She was 26 at the time. On the morning of 16 June 1963, Tereshkova and her backup Solovyova were both dressed in spacesuits and taken to the launch pad by bus. Following the tradition set by Gagarin, Tereshkova also urinated on the bus tire, becoming the first woman to do so. After completing her communication and life support checks, she was sealed inside the Vostok. After a two-hour countdown, Vostok 6 launched faultlessly, and Tereshkova became the first woman in space. Her call sign in this flight was Chaika (English: Seagull; ), later commemorated as the name of an asteroid, 1671 Chaika.
Although Tereshkova experienced nausea and physical discomfort for much of the flight, she orbited the earth 48 times and spent almost three days in space. With a single flight, she logged more flight time than the combined times of all American astronauts who had flown before that date. Tereshkova also maintained a flight log and took photographs of the horizon, which were later used to identify aerosol layers within the atmosphere.