Ann Elizabeth Packer MBE (born 8 March 1942 in Moulsford, Oxfordshire, UK) is a former British sprinter, hurdler and long jumper. She won a gold medal in the 800 metres at the 1964 Summer Olympics in Tokyo.

Ann Packer was a member of Reading Athletic Club when she was selected for the British team, and working as a physical education teacher. She was in the 4 x 100 metres relay team that won a silver medal in the 1962 Commonwealth Games and a bronze medal in the 1962 European Athletics Championships.

Packer travelled to Tokyo in 1964 where she shared a room with long jump gold medallist Mary Rand. Packer was hoping to win her favourite event, the 400 metres, but was beaten into second place by Betty Cuthbert of Australia, despite setting a new European record (52.2sec). After winning a silver medal in the 400 metres Packer had no plans to run in the 800 metres and had a shopping trip planned until her fiancé, Robbie Brightwell finished fourth in the 400 metres. Disappointed for him, she turned to the 800 metres, an event which she had only raced in five times before, and never in international competition. She had only taken up the longer race to improve her stamina, and earned the third British spot at the length at the last minute.