The Football Association had registered an expression of interest with FIFA, but has now decided to drop its bid.
France, South Korea, New Zealand and South Africa are still bidding to host the tournament.
FA sources said the decision was taken for varied reasons and not directly connected with recent difficult relations between the governing body and FIFA.
FA chairman Greg Dyke and England's UEFA executive committee member David Gill both stated earlier this month that FIFA president Sepp Blatter should not stand for a fifth term last year.
"The FA can confirm that it will not be progressing its initial interest in hosting either the FIFA Women's World Cup in 2019, or the Under-20 Women's World Cup in 2018, said Dyke
"Expressions of interest were lodged to gain a wider understanding of the bidding process, the benefits associated to the tournaments and the wider competition to host the tournaments.
"Having assessed all of these factors The FA will not be furthering it's interest in these competitions at this time."