Your question is somewhat ambiguous. Not counting youth tournaments such as the U-17 and U-20 World Cups, the youngest goalkeeper ever to start in a World Cup was Cecilia Santiago of Mexico, born 19 October 1994, in a 1–1 draw vs. England on 27 June 2011. She was 16 years and 251 days old.
At least one fifteen-year-old goalkeeper has sat on the bench in a World Cup, Yun Hyon-hi of North Korea in 2007. In fact, she was still a teenager when she got her first World Cup start in 2011.
Although I don't have a complete ranking by age in days, the rest of the top five are also women, or girls at the time. There are several teenage goalkeepers at every Women's World Cup (the first being Ann Chiejine, who was 17 when she played for Nigeria versus Germany on November 17, 1991), while there are no goalkeepers in FIFA's official list of the youngest men to ever play in a World Cup, which stops at 19 years, 4 months, and 21 days.